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Sun, 01 Mar 1998 00:00:00 +0000

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Sun, 01 Mar 1998 00:00:00 +0000

Technick.net is an original site created by Nicola Asuni, previously called Nick Homepage, online since:Sun, 1 March 1998 03:17:30 - 0800(PST).

DISCLAIMER

PLEASE BE AWARE THAT ANY INFORMATION YOU MAY FIND IN THIS WEBSITE MAY BE INACCURATE, MISLEADING OR DANGEROUS.

Some information on Technick.net may create an unreasonable risk for those readers who choose to apply or use the information in their own activities or to promote the information for use by third parties.

JSON Editor

Tue, 09 May 2017 00:00:00 +0000

JSON Editor

Load JSON Schema

Validation

This will update whenever the form changes to show validation errors if there are any.

JSON Output

You can also make changes directly to the JSON here.

Load

AWG to Metric Converter

Sun, 01 Mar 1998 00:00:00 +0000

Reference and sources:

Electronics

Sun, 01 Mar 1998 00:00:00 +0000

Hardware

Sun, 01 Mar 1998 00:00:00 +0000

Inductance Calculator

Sun, 01 Mar 1998 00:00:00 +0000

Select the box with the geometry that you would like to calculate.

Round-Wire geometries (loops of wire with various shapes)
Circular Loop	Rectangular Loop	Square Loop	Equilateral Triangle Loop	Isosceles Triangle Loop

Transmission Line geometries (cross sections) the values calculated are the inductance per unit length
Twin Lead	Round Wire over a Ground Plane	Vertically Spaced Traces	Wide Trace over a Ground Plane	Coplanar Traces

Morse Code Converter

Sun, 01 Mar 1998 00:00:00 +0000

Alphanumeric	Morse Code


Spelling

PCB Impedance and Capacitance Calculator

Sun, 01 Mar 1998 00:00:00 +0000

Select the box with the geometry that you would like to calculate.
Microstrip	Embedded Microstrip	Stripline	Dual Stripline
Asymmetric Stripline	Differential Impedance of Microstrip	Differential Impedance of Stripline

THESE FORMULAS ARE APPROXIMATIONS!
They should not be used when a high degree of accuracy is required.
The approximate formulas are provided along with restrictions on the relative size of the various parameters.

All the units are in SI (Iternational System):

[m] = meter
[s] = second
[H] = Henry
[F] = Farad

Software

Sun, 01 Mar 1998 00:00:00 +0000

Theory

Sun, 01 Mar 1998 00:00:00 +0000

Software Metrics

Tue, 23 Dec 2014 00:00:00 +0000

Introduction

Quantitative measurements are essential in all sciences, including computer science, as we can’t optimise what we can’t measure.

In this context the term “metric” and “measure” will be often used as synonymous, even if by definition metrics are functions, while measurements are the numbers obtained by the application of metrics.

Software metrics are used to record events taking place in the execution of a software program in order to obtain objective, reproducible and quantifiable measurements. These measures provide an audit trail that have numerous valuable applications, including understanding the activity, quality assurance testing, software debugging, software performance optimisation, cost estimation, budget planning, etc.

Software Naming

Wed, 19 Nov 2014 00:00:00 +0000

Introduction

Choosing a good name for a software project is a critical task, as it will be referenced multiple times in building pipelines, configurations, logs, documentation, deployment packages, software dependencies, emails, discussions, and early morning support calls.

To avoid common issues related to software names it is important to follow a convention that minimise incompatibilities between technologies, platforms and usage case scenarios.

Here is proposed a convention that works well in the aforementioned multiple situations.

Simple API JSON Response Format

Fri, 17 Oct 2014 00:00:00 +0000

Introduction

The JavaScript Object Notation (JSON) format is a widely adopted standard to deliver HTTP RESTful API responses. This mostly because of the following properties:

It is a standard open lightweight data-interchange format;
Along with XML is the main format for data interchange used on the modern web;
It is easy for humans to read and write;
It is easy for machines to parse and generate;
Supports all the basic data types (numbers, strings, boolean, arrays and hashes);
It is developer-friendly, as it can be generated and parsed from almost any programming languages;
Popular databases (e.g. MongoDB, MySQL, PostgreSQL) can store the JSON format natively.

Following a shared convention promotes reuse and helps increasing the productivity by leaving more time to focus on the actual development task. However, while there are many common patterns for structuring JSON-based HTTP/REST API responses, there is no consistency in things like naming or types of responses.

Software Configuration

Sat, 13 Sep 2014 00:00:00 +0000

Introduction

In this context for “configuration” we consider the set of initial parameter settings that are read at run-time by computer programs.

Traditionally the configuration data has been provided mostly in plain-text format but in recent years structured standards have gained more traction. This mostly because in modern distributed environments the configurations are often provided via a Configuration Management System (CMS), transmitted via network and consumed by multiple applications, or multiple instances of the same application. Additionally, some of the configuration parameters are often automatically determined by the CMS instead of being manually entered by humans.

Software Logging Format

Mon, 11 Aug 2014 00:00:00 +0000

Introduction

Logs are used to record events taking place in the execution of a software program in order to provide an audit trail that can be used to understand the activity and diagnose problems.

In modern distributed environments the logs produced by multiple applications, or multiple instances of the same application, are often collected and processed in a single place. A typical stack involves the use of Elasticsearch, Logstash and Kibana (ELK). In this environments the first level consumer of the log messages is not anymore a human but a machine. This mostly because humans cannot process information in the massive flows that are created by concurrent and distributed systems. This poses new challenges when using traditional plain-text log formats designed for human consumption:

Build Software with Docker

Mon, 07 Jul 2014 00:00:00 +0000

Introduction

Two of the major requirements for a Continuous Integration/Delivery system (CI/CD) are:

Isolation: the ability to run a well isolated environment from other builds executed on the same infrastructure;
Reproducibility : the ability to reproduce the build environment from a pre-defined setup.

These requirements also apply to local development environments, ensuring developers the ability of consistently reproduce building and testing processes.

A great way to bootstrap reproducible and isolated environments is using Docker containers.

Software Automation

Thu, 05 Jun 2014 00:00:00 +0000

Introduction

The software development and deployment cycle usually involves numerous and tedious steps other than just “coding”. These steps often includes: download dependencies, build with different options, run various static analysis tools to check if the project meets the minimum predefined set of quality metrics, execute unit tests and check code coverage, execute functional and other types of tests, generate documentation, packaging, etc.

The ability to run all the development steps easily and frequently in a consistent and automatic way is important to minimize human errors, improve the software quality and speeds up the whole development cycle.

Software Structure

Sat, 03 May 2014 00:00:00 +0000

This document illustrates a portable directory structure for software projects to promote reusability and simplify the development cycle.

The software development and deployment cycle usually involves numerous and tedious steps other than just "coding". Some steps can be automated by Integration or Continuous Delivery systems (CI/CD), others needs to be performed frequently on the development machine before committing the code. Common development steps often includes: download dependencies, run various static analysis tools to check if the project meets the minimum predefined set of quality metrics, execute unit tests and check code coverage, execute functional and integration tests, check or generate documentation, etc.

Software Versioning

Wed, 02 Apr 2014 00:00:00 +0000

This document illustrates a strategy used for versioning software projects that is portable across different languages and technologies.

Having a universal way of versioning software development projects is a good thing to help us keep track of what's going on.

From Wikipedia (https://en.wikipedia.org/wiki/Software_versioning): "Software versioning is the process of assigning either unique version names or unique version numbers to unique states of computer software. [...] Modern computer software is often tracked using two different software versioning schemes: an internal version number that may be incremented many times in a single day, such as a revision control number, and a released version that typically changes far less often, such as semantic versioning or a project code name."

Formatting bytes in a spreadsheet cell

Sat, 01 Mar 2014 00:00:00 +0000

The following is a cell function that can be used with a spreadsheet application (e.g. MS Excel or LibreOffice Calc) to format a cell number using byte multiples.

The example below uses the content of the cell A1 as input.

For an explanation of IEC Prefixes for binary multiples please consult the guide: Multiples and Submultiples Prefixes Tables.

=IF((A1>=POWER(2,80)), CONCATENATE(TEXT((A1/POWER(2,80)),"##0.00"), " YiB"), IF((A1>=POWER(2,70)), CONCATENATE(TEXT((A1/POWER(2,70)),"##0.00"), " ZiB"), IF((A1>=POWER(2,60)), CONCATENATE(TEXT((A1/POWER(2,60)),"##0.00"), " EiB"), IF((A1>=POWER(2,50)), CONCATENATE(TEXT((A1/POWER(2,50)),"##0.00"), " PiB"), IF((A1>=POWER(2,40)), CONCATENATE(TEXT((A1/POWER(2,40)),"##0.00"), " TiB"), IF((A1>=POWER(2,30)), CONCATENATE(TEXT((A1/POWER(2,30)),"##0.00"), " GiB"), IF((A1>=POWER(2,20)), CONCATENATE(TEXT((A1/POWER(2,20)),"##0.00"), " MiB"), IF((A1>=POWER(2,10)), CONCATENATE(TEXT((A1/POWER(2,10)),"##0.00"), " KiB"), CONCATENATE(TEXT((A1),"##0.00"), " B") ) ) ) ) ) ) ) )

Ammonium Persulfate: Etchant for copper-plated PC Boards

Sun, 01 Mar 1998 00:00:00 +0000

AMMONIUM PERSULFATE – (NH₄)₂S₂O₈
(ammonium peroxydisulfate; peroxydisulfuric acid, diammonium salt)
Description:

Colorless to light straw crystals or powder. Odorless.
Strong oxidizer.
Hazard classes: 5.1 oxidizer; 6.3 acute health hazard.
CAS No.: 7727-54-0
UN-NA No.: 1444

NFPA 704 Placarding Information:

Health – 2
Flammability – 0
Reactivity – 1
Special Notice – OX

Uses:

Oxidizer and bleaching agent.
Used in photography; electroplating; preserving food; depolorizing batteries; and washing infected yeast.
Etchant for printed circuit boards and copper.
In the manufacture of other persulfates, deodorizing and bleaching oils, and aniline dyes.

Reactivity and Fire Risk:

ASCII Table

Sun, 01 Mar 1998 00:00:00 +0000

ASCII = American Standard Code for Information Interchange
Dec Hex Char Description Dec Hex Char Dec Hex Char Dec Hex Char
0 0 NUL null 32 20 64 40 @ 96 60 `
1 1 SOH start of heading 33 21 ! 65 41 A 97 61 a
2 2 STX start of text 34 22 " 66 42 B 98 62 b
3 3 ETX end of text 35 23 # 67 43 C 99 63 c
4 4 EOT end of transmission 36 24 $ 68 44 D 100 64 d
5 5 ENQ enquiry 37 25 % 69 45 E 101 65 e
6 6 ACK acknowledge 38 26 & 70 46 F 102 66 f
7 7 BEL bell 39 27 ' 71 47 G 103 67 g
8 8 BS backspace 40 28 ( 72 48 H 104 68 h
9 9 TAB horizontal tab 41 29 ) 73 49 I 105 69 i
10 A LF NL line feed, new line 42 2A * 74 4A J 106 6A j
11 B VT vertical tab 43 2B + 75 4B K 107 6B k
12 C FF NP form feed, new page 44 2C , 76 4C L 108 6C l
13 D CR carriage return 45 2D - 77 4D M 109 6D m
14 E SO shift out 46 2E . 78 4E N 110 6E n
15 F SI shift in 47 2F / 79 4F O 111 6F o
16 10 DLE data link escape 48 30 0 80 50 P 112 70 p
17 11 DC1 device control 1 49 31 1 81 51 Q 113 71 q
18 12 DC2 device control 2 50 32 2 82 52 R 114 72 r
19 13 DC3 device control 3 51 33 3 83 53 S 115 73 s
20 14 DC4 device control 4 52 34 4 84 54 T 116 74 t
21 15 NAK negative acknowledge 53 35 5 85 55 U 117 75 u
22 16 SYN synchronous idle 54 36 6 86 56 V 118 76 v
23 17 ETB end of transmission block 55 37 7 87 57 W 119 77 w
24 18 CAN cancel 56 38 8 88 58 X 120 78 x
25 19 EM end of medium 57 39 9 89 59 Y 121 79 y
26 1A SUB substitute 58 3A : 90 5A Z 122 7A z
27 1B ESC escape 59 3B ; 91 5B [ 123 7B {
28 1C FS file separator 60 3C < 92 5C \ 124 7C |
29 1D GS group separator 61 3D = 93 5D ] 125 7D }
30 1E RS record separator 62 3E > 94 5E ^ 126 7E ~
31 1F US unit separator 63 3F ? 95 5F _ 127 7F DEL

AWG to Metric Conversion Chart

Sun, 01 Mar 1998 00:00:00 +0000

Reference and Sources:

Wikipedia: American wire gauge

American Wire Gauge (AWG) & Metric Wire Gauge Wire Sizes

Van den Hul: AWG to Metric Conversion Chart

This table gives closest equivalent size cross references between metric and American wire sizes. In Europe, wire sizes are expressed in cross sectional area in mm² and also as the number of strands of wires of a diameter expressed in mm. For example 7/0.2 means 7 strands of wire each 0.2mm diameter. This example has a cross sectional area of 0.22mm². In America, the commonest system is the AWG numbering scheme, where the numbers are applied not only to individual strands but also to equivalent size bunches of smaller strands. For example 24AWG could be made of 1 strands of 24AWG wire (1/24) or 7 strands of 32 AWG wire (7/32).

See also: AWG to metric Parameter Calculator.

Basic Soldering Guide

Sun, 01 Mar 1998 00:00:00 +0000

Types of Iron | How to Solder | How to Desolder | Summary | Trouble Shooting Guide | First Aid
Photo Gallery | Contacting the Author | Copyright & Disclaimer |

This written guide will help beginners and novices to obtain effective results when soldering electronic components. If you have little or no experience of using a soldering iron, then we recommend that you practice your soldering technique on some fresh surplus components and clean stripboard (protoboard), before experimenting with a proper constructional project. This will help you to avoid the risk of disappointment when you start to assemble your first prototypes. If you've never soldered before, then read on!

Types of Iron

Topics in this section include: Voltage, Wattage, Temperature Control, Soldering Stations, Anti-Static Protection, Bits (Tips), Spare Parts, and Gas-Powered Irons.
The most fundamental skill needed to assemble any electronic project is that of soldering. It takes some practice to make the perfect joint, but, like riding a bicycle, once learned is never forgotten! The idea is simple: to join electrical parts together to form an electrical connection, using a molten mixture of lead and tin (solder) with a soldering iron. A large range of soldering irons is available -- which one is suitable for you depends on your budget and how serious your interest in electronics is.

Electronics catalogues often include a selection of well-known brands of soldering iron. Excellent British-made ones include the universally popular Antex, Adcola and Litesold makes. Other popular brands include those made by Weller and Ungar. A very basic mains electric soldering iron can cost from under 5 UK Pounds (8 US Dollars), but you can expect a reasonable model to be approximately 10 to 12 UKP (16 to 20 US Dollars), and it's quite possible to spend into three figures on a "soldering station" if you're really serious! You can check suppliers' catalogues for some typical types of iron. Certain factors you need to bear in mind include:

Voltage: Most irons run from the mains at 240V (110V in the US). However, low voltage types (e.g.
12V or 24V) generally form part of a "soldering station," and are designed to be used with a special controller made by the same manufacturer.

Wattage: Typically, soldering irons may have a power rating of between 15-25 watts or so, which is fine for most work. A higher wattage does not mean that the iron runs hotter -- it simply means that there is more power in reserve for coping with larger joints. This also depends partly on the design of the "bit" (the tip of the iron). Consider a higher wattage iron simply as being more "unstoppable" when it comes to heavier-duty work, because it won't cool down so quickly.

Temperature Control: The simplest and cheapest types don't have any form of temperature regulation. Simply plug them in and switch them on! Thermal regulation is "designed in" (by physics, not electronics!). These irons may be described as "thermally balanced" so that they have some degree of temperature "matching," but their output will otherwise not be controlled. Unregulated irons form an ideal general purpose iron for most users, and they generally cope well with printed circuit board soldering and general interwiring. Most of these "miniature" types of iron will be of little use when attempting to solder large joints (e.g. very large terminals or very thick wires) because the component being soldered will "sink" heat away from the tip of the iron, cooling it down too much. (This is where a higher wattage comes in useful.)

A proper temperature-controlled iron will be quite a lot more expensive -- retailing at say 40 UKP (60 USD) or more. This type of iron will have some form of built-in thermostatic control, to ensure that the temperature of the bit (the tip of the iron) is maintained at a fixed level (within limits). This is desirable, especially during more frequent use, since it helps to ensure that the temperature does not "overshoot" in between times, and also guarantees that the output will be relatively stable. Some irons have a bimetallic strip thermostat built into the handle which gives an audible "click" in use: other types use all-electronic controllers, and some may be adjustable using a screwdriver.

Yet more expensive still, soldering stations cost from 70 UKP (115 USD) upwards (the iron may
be sold separately, so you can pick the type you prefer). Soldering stations consist of a complete bench-top control unit into which a special low-voltage soldering iron is plugged. Some versions might have a built-in digital temperature readout, and will have a control knob to enable you to vary the setting. The temperature could be boosted for soldering larger joints, for example, or for using higher melting-point solders (e.g. silver solder). These are designed for the most discerning users, or for continuous production line and professional use. The best stations have irons which are well balanced, with comfort-grip handles which remain cool all day. A thermocouple will be built into the tip or shaft, which monitors temperature.

Anti-Static Protection: If you're interested in soldering a lot of static-sensitive parts (e.g. CMOS chips or MOSFET transistors), more advanced and expensive soldering iron stations use static-dissipative
materials in their construction to ensure that static does not build up on the iron itself. You may see these listed as "ESD safe" (electrostatic discharge proof). The cheapest irons won't necessarily be ESD-safe but never the less will still probably perform perfectly well in most hobby or educational applications if you take the usual anti-static precautions when handling the components. The tip would need to be well earthed (grounded) in these circumstances.

Bits: It's useful to have a small selection of manufacturer's bits (soldering iron tips) available with different diameters or shapes, which can be changed depending on the type of work in hand. You'll probably find that you become accustomed to, and work best with, a particular shape of tip. Often, tips are iron-coated to preserve their life, or they may be bright-plated instead. Copper tips are seldom seen these days.

Spare Parts: it's nice to know that spare parts may be available, so if the element blows, you don't need to replace the entire iron. This is especially so with expensive irons. Check through some of the larger mail-order catalogues.

Gas-Powered Irons: You will occasionally see gas-powered soldering irons which use butane rather than the mains electrical supply to operate. They have a catalytic element which, once warmed up, continues to glow hot when gas passes over them. Service engineers use them for working on repairs where there may be no power available, or where a joint is tricky to reach with a normal iron, so they are really for occasional "on the spot" use for quick repairs, rather than for mainstream construction or assembly work.

Basics of Electrostatic Discharge (ESD)

Sun, 01 Mar 1998 00:00:00 +0000

Batteries in a Portable World 2nd Ed.

Sun, 01 Mar 1998 00:00:00 +0000

Controlling Electrical Hazards

Sun, 01 Mar 1998 00:00:00 +0000

This article provides an overview of basic electrical safety for individuals with little or limited training or familiarity with electrical hazards. The concepts and principles presented will help further an understanding of OSHA's electrical safety standards for general industry, Title 29 Code of Federal Regulations (CFR), Part 1910.302, Sub-part S-Design Safety Standards for Electrical Systems, and 1910.331 Electrical Safety-Related Work Practices Standard (1990).

Contents / Menu
Introduction
How Electricity Acts?
How Shocks Occur?
Severity of the Shock
Burns and Other Injuries
Preventing Electrical Hazards
( Insulation, Guarding, Grounding, Circuit Protection Devices, Safe Work Practices, Training, Overhead Lines )
Conclusion

Definitions of the SI base and derived units

Sun, 01 Mar 1998 00:00:00 +0000

(Definitions of the SI base units, SI derived units, Other not SI units)
The International System of Units, universally abbreviated SI (from the French Le Système International d'Unités), is the modern metric system of measurement. The SI was established in 1960 by the 11th General Conference on Weights and Measures (CGPM, Conférence Générale des Poids et Mesures). The CGPM is the international authority that ensures wide dissemination of the SI and modifies the SI as necessary to reflect the latest advances in science and technology.

Dielectric Constants of Material

Sun, 01 Mar 1998 00:00:00 +0000

Reference and Sources:
Zed Z. Chang
Material Min. Max.
Air 1 1
Amber 2.6 2.7
Asbestos fiber 3.1 4.8
Bakelite 5 22
Barium Titanate 100 1250
Beeswax 2.4 2.8
Cambric 4 4
Carbon Tetrachloride 2.17 2.17
Celluloid 4 4
Cellulose Acetate 2.9 4.5
Durite 4.7 5.1
Ebonite 2.7 2.7
Epoxy Resin 3.4 3.7
Ethyl Alcohol 6.5 25
Fiber 5 5
Formica 3.6 6
Glass 3.8 14.5
Glass Pyrex 4.6 5
Gutta Percha 2.4 2.6
Isolantite 6.1 6.1
Kevlar 3.5 4.5
Lucite 2.5 2.5
Mica 4 9
Micarta 3.2 5.5
Mycalex 7.3 9.3
Neoprene 4 6.7
Nylon 3.4 22.4
Paper 1.5 3
Paraffin 2 3
Plexiglass 2.6 3.5
Polycarbonate 2.9 3.2
Polyethylene 2.5 2.5
Polyimide 3.4 3.5
Polystyrene 2.4 3
Porcelain 5 6.5
Quartz 5 5
Rubber 2 4
Ruby Mica 5.4 5.4
Selenium 6 6
Shellac 2.9 3.9
Silicone 3.2 4.7
Slate 7 7
Soil dry 2.4 2.9
Steatite 5.2 6.3
Styrofoam 1.03 1.03
Teflon 2.1 2.1
Titanium Dioxide 100 100
Vaseline 2.16 2.16
Vinylite 2.7 7.5
Water distilled 34 78
Waxes, Mineral 2.2 2.3
Wood dry 1.4 2.9

Digital Audio Resampling

Sun, 01 Mar 1998 00:00:00 +0000

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "The Digital Audio Resampling Home Page", by Julius O. Smith III, Copyright © 2016-05-17 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Elementary Digital Filter Theory

Sun, 01 Mar 1998 00:00:00 +0000

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Introduction to Digital Filters with Audio Applications", by Julius O. Smith III, Copyright © 2017-11-26 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Ferric Chloride Solution: Etchant for copper-plated PC Boards

Sun, 01 Mar 1998 00:00:00 +0000

Ferric Chloride CAS #7705-08-0 Green-black solution in water with a mild acid-like odor. May cause eye and skin burns. May be harmful if swallowed. Ingestion may cause rapid heartbeat, low blood pressure, shock, and possible coma. May cause kidney and liver damage. Inhalation of vapor may cause severe respiratory tract irritation. Substance has caused adverse reproductive effects in animals. Target Organs: Kidneys, liver, cardiovascular system. Adverse Health Effects If in Eyes: May cause eye burns. Contact produces irritation, tearing, and burning pain. If on Skin: May be absorbed through the skin. May cause severe irritation and possible burns. If Swallowed: May cause irritation of the digestive tract. May cause liver and kidney damage. Causes severe pain, nausea, vomiting, diarrhea, and shock. May cause severe irritation of the mouth and throat. May cause low blood pressure, rapid heartbeat, skin discoloration, and possible coma. If Inhaled: Vapor may cause severe respiratory tract irritation. Prolonged or repeated exposure may cause adverse reproductive effects. Repeated exposure may increase an increased body load of iron. FIRST AID MEASURES: Eyes: Immediately flush eyes with plenty of water for at least 15 minutes, occasionally lifting the upper and lower lids. Get medical aid immediately. Do NOT allow victim to rub or keep eyes closed. Skin: Immediately flush skin with plenty of soap and water for at least 15 minutes while removing contaminated clothing and shoes. Get medical aid if irritation develops or persists. Ingestion: If victim is conscious and alert, give 2-4 cupfuls of milk or water. Get medical aid immediately. Inhalation: Remove from exposure to fresh air immediately. If not breathing, give artificial respiration. If breathing is difficult, give oxygen. Get medical aid. Notes to Physician: Treat symptomatically and supportively. The use of an iron chelator should be determined only by qualified medical personnel. Handling: Wash thoroughly after handling. Remove contaminated clothing and wash before reuse. Use with adequate ventilation. Do not get in eyes, on skin, or on clothing. Do not ingest or inhale. Storage: Do not store in direct sunlight. Store in a cool, dry, well-ventilated area away from incompatible substances. OSHA Vacated PELs: Ferric Chloride: No OSHA Vacated PELs are listed for this chemical.
Physical State: Liquid Appearance: Green-black solution. Odor: Mild acid-like. pH: 2.0 (0.1M sol.) Vapor Pressure: Not available. Vapor Density: Not available. Evaporation Rate: Not available. Viscosity: Not available. Boiling Point: 212 degrees F Freezing/Melting Point: Not available. Decomposition Temperature: Not available. Solubility: Soluble in water. Specific Gravity/Density: 1.4 (water=1) Molecular Formula: FeCl3 Molecular Weight: 162.206 Chemical Stability: Stable under normal temperatures and pressures. Incompatible with Alkalis, allyl chloride, ethylene oxide, nylon, oxidizers, potassium, sodium. Corrosive to most metals. Hazardous Decomposition Products: Hydrogen chloride, chlorine. Hazardous Polymerization: None reported. LD50/LC50: CAS# 7732-18-5: Oral, rat: LD50 = >90 mL/kg. CAS# 7732-18-5: Oral, rat: LD50 = >90 mL/kg. Carcinogenicity: Not listed by ACGIH, IARC, NIOSH, NTP, or OSHA. Epidemiology: No information available. Teratogenicity: No information available. Reproductive Effects: Fertility: Pre-implantation mortality, intravaginal-rat TDLo=29mg/kg. Paternal Effects: Spermatogenesis and Testes/sperm duct/epididymis, intratesticular-rat TDLo=12976ug/kg. Neurotoxicity: No information available. Mutagenicity: No information available. Other Studies: None. Ecotoxicity: Daphnia (fresh water) TLm=15ppm/96H Mosquito fish TLm=74ppm/96H Minnow TLm=540ppm/1.5H Environmental Fate: No information available. Dispose of in a manner consistent with federal, state, and local regulations. RCRA D-Series Maximum Concentration of Contaminants: Not listed. RCRA D-Series Chronic Toxicity Reference Levels: Not listed. RCRA F-Series: Not listed. RCRA P-Series: Not listed. RCRA U-Series: Not listed. Not listed as a material banned from land disposal according to RCRA. Transportation Information: Shipping Name: FERRIC CHLORIDE SOLUTION Hazard Class: 8(9.2) UN Number: UN2582 TSCA: CAS# 7705-08-0 is listed on the TSCA inventory. Not listed on the Health & Safety Reporting List. Not listed under TSCA Section 12b. Does not have a SNUR under TSCA. CERCLA/SARA: Section 302 (RQ) NONE Section 302 (TPQ) NONE Section 313 Not reportable under Section 313. Clean Air Act: This material does not contain any hazardous air pollutants. This material does not contain any Class 1 Ozone depletors. This material does not contain any Class 2 Ozone depletors. Clean Water Act: CAS# 7705-08-0 is listed as a Hazardous Substance under the CWA. Not are listed as Priority Pollutants under the CWA. Not listed as Toxic Pollutants under the CWA. OSHA: Not are considered highly hazardous by OSHA. Ferric Chloride can be found on the following state right to know lists: New Jersey, Pennsylvania, Massachusetts. Not present on state lists from CA, PA, MN, MA, FL, or NJ. California No Significant Risk Level: Not listed. Canada CAS# 7705-08-0 is listed on Canada’s DSL/NDSL List. CAS# 7705-08-0 is not listed on Canada’s Ingredient Disclosure List. European Labeling in Accordance with EC Directives Hazard Symbols: Not available. Risk Phrases: Not available. Safety Phrases: Not available. Exposure Limits: OEL-DENMARK:TWA 1 mg(Fe)/m3 JANUARY 1993. OEL-FINLAND:TWA 1 mg(Fe)/m3 JANUARY 1993. OEL-THE NETHERLANDS:TWA 1 mg(Fe)/m3 JANUARY 1993. OEL-SWITZERLAND:TWA 1 mg(Fe)/m3 JANUARY 1993. OEL-UNITED KINGDOM:TWA 1 mg(Fe)/m3;STEL 2 mg(Fe)/m3 JANUARY 1993. OEL IN BULGARIA, COLOMBIA, JORDAN, KOREA check ACGIH TLV. OEL IN NEW ZEALAND, SINGAPORE, VIETNAM check ACGI TLV

Back to PCBs Fabrication Methods Guide

Inductance of Circular Loop

Sun, 01 Mar 1998 00:00:00 +0000

Loop of wire with circular shape
N [ ] number of turns
R [m] radius of the circle
a [m] wire radius
µ_r [ ] relative permeability of the medium
L [H] Inductance

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 H = 1.1427·10^-9 H = 1.427 nH)

Inductance of Coplanar Traces

Sun, 01 Mar 1998 00:00:00 +0000

Cross section of Coplanar Traces transmission line
w [m] width of the traces
d [m] center-to-center distance
t [m] thickness of the traces
µ_r [ ] relative permeability of the medium
L/l [H/m] Inductance per unit length

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 H = 1.1427·10^-9 H = 1.427 nH)

See also notes on Inductance Calculations page.

Inductance of Equilateral Triangle Loop

Sun, 01 Mar 1998 00:00:00 +0000

Loop of wire with Equilateral Triangle shape
N [ ] number of turns
s [m] length of one side
a [m] wire radius
µ_r [ ] relative permeability of the medium
L [H] Inductance

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 H = 1.1427·10^-9 H = 1.427 nH)

See also notes on Inductance Calculations page.

Inductance of Isosceles Triangle Loop

Sun, 01 Mar 1998 00:00:00 +0000

Loop of wire with Isosceles Triangle shape
N [ ] number of turns
b [m] length of the base
c [m] length of the equal sides
a [m] wire radius
µ_r [ ] relative permeability of the medium
L [H] Inductance

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 H = 1.1427·10^-9 H = 1.427 nH)

See also notes on Inductance Calculations page.

Inductance of Rectangular Loop

Sun, 01 Mar 1998 00:00:00 +0000

Loop of wire with rectangular shape
N [ ] number of turns
w [m] width of the rectangle
h [m] height of the rectangle
a [m] wire radius
µ_r [ ] relative permeability of the medium
L [H] Inductance

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 H = 1.1427·10^-9 H = 1.427 nH)

See also notes on Inductance Calculations page.

Inductance of Round Wire over a Ground Plane

Sun, 01 Mar 1998 00:00:00 +0000

Cross section of Round Wire transmission line over a Ground Plane
h [m] height of center from ground plane
a [m] wire radius
µ_r [ ] relative permeability of the medium
L/l [H/m] Inductance per unit length

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 H = 1.1427·10^-9 H = 1.427 nH)

See also notes on Inductance Calculations page.

Inductance of Square Loop

Sun, 01 Mar 1998 00:00:00 +0000

Loop of wire with square shape
N [ ] number of turns
w [m] width of the rectangle
a [m] wire radius
µ_r [ ] relative permeability of the medium
L [H] Inductance

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 H = 1.1427·10^-9 H = 1.427 nH)

See also notes on Inductance Calculations page.

Inductance of Twin Lead

Sun, 01 Mar 1998 00:00:00 +0000

Cross section of Twin Lead transmission line
d [m] distance from center to center
a [m] wire radius
µ_r [ ] relative permeability of the medium
L/l [H/m] Inductance per unit length

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 H = 1.1427·10^-9 H = 1.427 nH)

See also notes on Inductance Calculations page.

Inductance of Vertically Spaced Traces

Sun, 01 Mar 1998 00:00:00 +0000

Cross section of Vertically Spaced Traces transmission line
w [m] width of the traces
h [m] center-to-center spacing of traces
t [m] thickness of the traces
µ_r [ ] relative permeability of the medium
L/l [H/m] Inductance per unit length

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 H = 1.1427·10^-9 H = 1.427 nH)

See also notes on Inductance Calculations page.

Inductance of Wide Trace over a Ground Plane

Sun, 01 Mar 1998 00:00:00 +0000

Cross section of Wide Trace transmission line over a Ground Plane
w [m] width of the trace
h [m] height of the trace above ground
t [m] thickness of the trace
µ_r [ ] relative permeability of the medium
L/l [H/m] Inductance per unit length

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 H = 1.1427·10^-9 H = 1.427 nH)

See also notes on Inductance Calculations page.

Mathematics of the Discrete Fourier Transform (DFT)

Sun, 01 Mar 1998 00:00:00 +0000

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Mouse Cleaning

Sun, 01 Mar 1998 00:00:00 +0000

When you run your mouse over the desktop it picks up all kinds of debris, gunk, and goo that can get drawn up into the insides of the mouse and cause it to stop working well.
If you find that the pointer on the screen doesn't move smoothly or that the trackball inside the mouse doesn't move freely, you should clean the mouse.

You could go to a computer store and buy one of those fancy mouse-cleaning kits, but, in my opinion, there really isn't any need. You're going to be able to clean it as well as anything using these inexpensive items:

Few clean cotton swabs.
Denatured alcohol. (I recommend denatured alcohol over rubbing alcohol, which has glycerine in it and can leave some slippery residue behind).
Water.
Mild soap.
A clean, soft, lint-free cloth (100% cotton works best).
An old toothbrush.
To clean your mouse, follow these steps:

1. Shut down and turn off your computer.

2. Disconnect the mouse cable from the computer.

3. Remove the trackball

3.1 Turn your mouse upside down.
3.2 Unlock the disk that's holding the trackball in place by either rotate counter-clockwise or slide in one direction.
3.3 Turn the mouse right side up with one hand and catch the ring and trackball with your other hand. Give it a shake if they don't dislodge themselves.

4. Wash the trackball and the retainer ring with warm soapy water using an old toothbrush. Rub the trackball thoroughly to remove any oily build-up.

5. Dry the trackball and the retainer ring thoroughly with a clean lint-free cloth.

6. Set the trackball and the retainer ring aside.

7. Moisten a lint-free cloth with denatured alcohol and gently rub the mouse back surface and trackball compartment. Blow into the trackball compartment to remove any dust or lint from inside.

8. Take a close look at the three rollers inside the mouse. You'll probably see lines of dirt that have accumulated over many months or even years of usage. These lines of dirt build up and cause jerky or erratic mouse movements. Clean the three small rollers inside the mouse with a cotton swab moistened with denatured alcohol. The cotton should be just a little damp. Rotate the rollers to clean all around them. Work the tip along each roller side to side until the line of dirt disappears. If there is a build-up of material on the rollers which the cotton swab does not remove, you can use your fingernail or a tweezer to gently remove the material.
WARNING: The rollers must remain smooth so be very careful not to gouge them with anything!

9. When it's clean, let it dry out for a moment or two.

10. Put the trackball back into the mouse and close the mouse trackball cover with a clockwise motion.

11. Reconnect the mouse cable to the computer.

12. Restart your computer and test mouse's movement.

13. Your mouse should be as good as new.

NOTE: Always use a clean mouse pad, free from dust, when moving your mouse.

Multiples and Submultiples Prefixes Tables

Sun, 01 Mar 1998 00:00:00 +0000

(SI Prefixes Table, IEC Prefixes for binary multiples)
SI Prefixes Table
The International System of Units, universally abbreviated SI (from the French Le Système International d'Unités), is the modern metric system of measurement.
The 20 SI prefixes used to form decimal multiples and submultiples of SI units are:
Symbol Name Factor Symbol Name Factor
Y yotta 10²⁴ y yokto 10^-24
Z zetta 10²¹ z zepto 10^-21
E exa 10¹⁸ a atto 10^-18
P peta 10¹⁵ f femto 10^-15
T tera 10¹² p pico 10^-12
G giga 10⁹ n nano 10^-9
M mega 10⁶ µ micro 10^-6
k kilo 10³ m milli 10^-3
h hecto 10² c centi 10^-2
da deka 10¹ d deci 10^-1
It is important to note that the kilogram is the only SI unit with a prefix as part of its name and symbol. Because multiple prefixes may not be used, in the case of the kilogram the prefix names of Table are used with the unit name "gram" and the prefix symbols are used with the unit symbol "g." With this exception, any SI prefix may be used with any SI unit, including the degree Celsius and its symbol °C.

Networking

Sun, 01 Mar 1998 00:00:00 +0000

On Cables and Connections

Sun, 01 Mar 1998 00:00:00 +0000

The original On Cables and Connections - A discussion by Dr. J. Kramer is Copyright © KRAMER ELECTRONICS LTD. (www.kramerelectronics.com). All rights reserved. No part of this publication may be reproduced, transmitted, transcribed, stored in a retrieval system or translated into any language or computer language in any form or by any means without written permission of KRAMER ELECTRONICS LTD. Sapir Center, Building 5, Jerusalem 95461, Israel - TEL:(972-2)-6524715, FAX:(972-2)-6535369 - Email: [email protected]">[email protected] This is a personalized version reproduced by permission.
Introduction
Rules-of-thumb to prevent cable problems
Cable length and quality
Solving cable related problems
When longer distances are needed
Line Amplifiers
The twisted-pair solution
The fiber-optic solution
The RF solution
Problems related to audio wires
Dealing with high capacitance audio wires
Dealing with noise pickup
Signal loss and deterioration due to cable impedance
Dealing with amplifier output quality degradation due to cable resistance
A final word

Passive Components Codes Guide

Sun, 01 Mar 1998 00:00:00 +0000

Codes for Resistors, Capacitors, Inductors, Termistors NTC and PTC, Varistors VDR.
Pictures
Color Code
Alpha-Numeric Code
One Letter Code
Pictures
Resistors

5 Band Ceramic Capacitors

Radial or Ayial Lead Ceramic Capacitors (6 Dot or Band System)

Ceramic Disk Capacitors

Ceramic Feed Through Capacitors

Dipped Tantalum Capacitors

Film Type Capacitors

5 Dot or Band Ceramic Capacitors (one wide band)

Postage Stamp Mica Capacitors

Standard Button Mica Capacitors

Polistirene Capacitors

Electrolitic Tantalum Capacitors (4 colors code)

Electrolitic Tantalum Capacitors (3 colors code)

Ceramic Capacitors Class II

Ceramic Capacitors Class I

Ceramic Capacitors Pin-up

PCB Impedance and Capacitance of Asymmetric Stripline

Sun, 01 Mar 1998 00:00:00 +0000

W [m] width of the trace
H [m] height of trace above return plane
H1 [m] height of trace above return plane
T [m] trace thickness
E_r [ ] relative permittivity of the dielectric

Are there distributed capacitive loads on this trace?
NoYes
L_a [m] average length of the traces attaching the loads
C_a [pF] average load capacitance

OUTPUT
Z₀ [Ohm] characteristic impedance
C₀ [F/m] capacitance per unit length
t_pd [s/m] propagation delay
L₀ [H/m] inductance per unit length
Z_c [Ohm] effective characteristic impedance
t'_pd [s/m] effective propagation delay

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 s/m = 1.1427·10^-9 s/m = 1.427 ns/m)

CONDITIONS: (0.1 < W/H < 2.0); ( T/H < 0.25);

PCB Impedance and Capacitance of Differential Microstrip

Sun, 01 Mar 1998 00:00:00 +0000

Z₀ [Ohm] characteristic impedance
H [m] height of trace above return plane
S [m] space between traces

OUTPUT
Z_d [Ohm] differential impedance

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 s/m = 1.1427·10^-9 s/m = 1.427 ns/m)
Formulas:

See also notes on PCB Impedance and Capacitance Calculator page.

PCB Impedance and Capacitance of Differential Stripline

Sun, 01 Mar 1998 00:00:00 +0000

Z₀ [Ohm] characteristic impedance
H [m] height of trace above return plane
S [m] space between traces

OUTPUT
Z_d [Ohm] differential impedance

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 s/m = 1.1427·10^-9 s/m = 1.427 ns/m)
Formulas:

See also notes on PCB Impedance and Capacitance Calculator page.

PCB Impedance and Capacitance of Dual Stripline

Sun, 01 Mar 1998 00:00:00 +0000

W [m] width of the trace
H [m] height of trace above return plane
T [m] trace thickness
C [m] distance between the differential stripline pair
E_r [ ] relative permittivity of the dielectric

Are there distributed capacitive loads on this trace?
NoYes
L_a [m] average length of the traces attaching the loads
C_a [pF] average load capacitance

OUTPUT
Z₀ [Ohm] characteristic impedance
C₀ [F/m] capacitance per unit length
t_pd [s/m] propagation delay
L₀ [H/m] inductance per unit length
Z_c [Ohm] effective characteristic impedance
t'_pd [s/m] effective propagation delay

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 s/m = 1.1427·10^-9 s/m = 1.427 ns/m)

CONDITIONS: (0.1 < W/H < 2.0); ( T/H < 0.25);

PCB Impedance and Capacitance of Embedded Microstrip

Sun, 01 Mar 1998 00:00:00 +0000

W [m] width of the trace
H [m] height of trace above return plane
H1 [m] height of dielectric above return plane
T [m] trace thickness
E_r [ ] relative permittivity of the dielectric

Are there distributed capacitive loads on this trace?
NoYes
L_a [m] average length of the traces attaching the loads
C_a [pF] average load capacitance

OUTPUT
Z₀ [Ohm] characteristic impedance
C₀ [F/m] capacitance per unit length
t_pd [s/m] propagation delay
L₀ [H/m] inductance per unit length
Z_c [Ohm] effective characteristic impedance
t'_pd [s/m] effective propagation delay

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 s/m = 1.1427·10^-9 s/m = 1.427 ns/m)

CONDITIONS: ( H1 > 1.2 H);

PCB Impedance and Capacitance of Microstrip

Sun, 01 Mar 1998 00:00:00 +0000

W [m] width of the trace
H [m] height of dielectric above return plane
T [m] trace thickness
E_r [ ] relative permittivity of the dielectric

Are there distributed capacitive loads on this trace?
NoYes
L_a [m] average length of the traces attaching the loads
C_a [pF] average load capacitance

OUTPUT
Z₀ [Ohm] characteristic impedance
C₀ [F/m] capacitance per unit length
t_pd [s/m] propagation delay
L₀ [H/m] inductance per unit length
Z_c [Ohm] effective characteristic impedance
t'_pd [s/m] effective propagation delay

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 s/m = 1.1427·10^-9 s/m = 1.427 ns/m)

CONDITIONS: ( 0.1 < W/H < 3.0);

PCB Impedance and Capacitance of Stripline

Sun, 01 Mar 1998 00:00:00 +0000

W [m] width of the trace
H [m] height of trace above return plane
T [m] trace thickness
E_r [ ] relative permittivity of the dielectric

Are there distributed capacitive loads on this trace?
NoYes
L_a [m] average length of the traces attaching the loads
C_a [pF] average load capacitance

OUTPUT
Z₀ [Ohm] characteristic impedance
C₀ [F/m] capacitance per unit length
t_pd [s/m] propagation delay
L₀ [H/m] inductance per unit length
Z_c [Ohm] effective characteristic impedance
t'_pd [s/m] effective propagation delay

NOTE: numbers are in scientific notation (e.g.: 1.427e-9 s/m = 1.1427·10^-9 s/m = 1.427 ns/m)

CONDITIONS: (0.1 < W/H < 2.0); ( T/H < 0.25);

PCBs Fabrication Methods

Sun, 01 Mar 1998 00:00:00 +0000

Printed Circuit Board (PCB) is a mechanical assembly consisting of layers of fiberglass sheet laminated with etched copper patterns. It is used to mount electronic parts in a rigid manner suitable for packaging. Also known as a Printed Wiring Board (PWB).
[Project] [Different methods to make PCBs] [Final work] [Bibliography/Reference]

Project
[Electric Scheme] [Part List - Bill of Materials] [Choose components from Data Sheets] [Choose Board type and dimension] [Draw the PCB layout] [Draw Fabrication scheme] [Draw Assembly scheme]

POST Beep Codes

Sun, 01 Mar 1998 00:00:00 +0000

When you turn the computer on, it performs Power On System Test (POST), during which it checks and initializes the system's internal components.
If a serious error occurs, the computer does not display a message but emits a series of long and short beeps instead.
Beeps are your computer's way of letting you know what's going on when the video signal is not working.
These codes are built in to the BIOS of the PC.
There is no official standard for these codes due to the many brands of BIOS that are out there.

To decode the meaning of your computer POST beep codes you must consult the manual of your motherboard.
If you don't have a motherboard manual or if it's incomplete you must search on the site of your computer manufacturer.
Another way is take off the computer case and look for BIOS manufacturer (just see if it says "AMI" or "Phoenix" ...).
For more information about BIOS and how to identify it please check this site: Wim's BIOS Page - Everything you want to know about BIOS.
Once you have determined your BIOS make, consult the following tables to see what's wrong with your computer.

RAID Technology

Sun, 01 Mar 1998 00:00:00 +0000

Reference and Sources:
The most part of text in this guide has been taken from copyrighted document of Adaptec, Inc. on site (www.adaptec.com)
Perceptive Solutions, Inc.
RAID stands for Redundant Array of Inexpensive (or sometimes "Independent") Disks.

RAID is a method of combining several hard disk drives into one logical unit (two or more disks grouped together to appear as a single device to the host system). RAID technology was developed to address the fault-tolerance and performance limitations of conventional disk storage. It can offer fault tolerance and higher throughput levels than a single hard drive or group of independent hard drives. While arrays were once considered complex and relatively specialized storage solutions, today they are easy to use and essential for a broad spectrum of client/server applications.

SCSI Technology

Sun, 01 Mar 1998 00:00:00 +0000

SCSI stands for Small Computer System Interface.
A standard for high-speed connections to peripherals.
[Source and Reference] [History] [Usage] [SCSI Hard Drives] [APPLE SCSI] [Hardware] [Single Ended or Differential] [Cabling] [SCSI Termination][SCSI Connectors]

Source and Reference
comp.periphs.scsi FAQ
ANSI T10 Technical Commitee Archive (SCSI draft spec's)
SCSI Trade Association
Adaptec, Inc.
Gary Field's SCSI Info Central

History
SCSI has it's roots in the mainframe world, but it's first implementation in the PC world came soon after the first PC. Shugart Associates devised an interface that they designated the SASI, or "Shugart Associates Standard Interface" They proposed that SASI be adopted by ANSI for small computers, but during the work required for ratification, they discovered the process would take too much effort, and that the IPI groups were already well into their effort. (which had many features the same as SASI) A decision was made to take features of both interfaces, and put forth a new specification for a new interface, SCSI was born, and ratified in 1986 by ANSI. Since then, many have said that the original spec. was not tight enough, and that it allowed Manufacturers to make drives that met the ANSI spec., but would not talk to each other. Recently, the ANSI SCSI committee has proposed newer, tighter, more extended specs., for SCSI-2, and now SCSI-3.

SODIUM METASILICATE, PENTAHYDRATE

Sun, 01 Mar 1998 00:00:00 +0000

Reference and Sources:
Rhodia

1. PRODUCT DESCRIPTION
Chemical Name or Synonym: DISODIUM TRIOXOSILICATE, PENTAHYDRATE ; CRYSTAMET
Molecular Formula: Na₂SiO_3^.nH₂O n=5

2. COMPOSITION/INFORMATION ON INGREDIENTS

Component CAS Reg Number OSHA
Hazard Percentage

SODIUM METASILICATE 6834-92-0 Y 100

3. HAZARDS IDENTIFICATION
A. EMERGENCY OVERVIEW:
Physical Appearance and Odor:
white granules solid, odorless.
Warning Statements:
DANGER! CAUSES SEVERE BURNS.

B. POTENTIAL HEALTH EFFECTS:
Acute Eye:
Corrosive. Causes burns, irritation.
Acute Skin:
Corrosive. Causes burns.
Acute Inhalation:
May cause upper respiratory tract irritation, dizziness, headache, shortness of breath, chest pain, muscle weakness, nausea, vomiting, serious damage to lung tissue and respiratory tract.
Acute Ingestion:
Causes nausea, vomiting, abdominal pain, chest pain, burns to mouth and esophagus.
Chronic Effects:
This product does not contain any ingredient designated by IARC, NTP, ACGIH or OSHA as probable or suspected human carcinogens.

Standard Certification Marks

Sun, 01 Mar 1998 00:00:00 +0000

[VDE Testing and Certification Institute] [Underwriters Laboratories Inc.] [CSA International] [NEMKO] [DEMKO] [FIMKO] [SEMKO] [VARIOUS]
VDE Testing and Certification Institute
Mark Description
VDE Mark for appliances as technical equipment according to the Appliance Safety Law (GSG), for Medical Device Law (MPG), components and installation materials.The VDE Mark indicates conformity with the VDE standards or European or internationally harmonized standards resp. and confirms compliance with protective requirements of the applicable EC Directive(s). The VDE Mark is a symbol for electrical, mechanical, thermal, toxic, radiological and other hazards.
For appliances as technical equipment according to the GSG.For ready-to-use equipment, the licence holder may chose to affix the VDE Mark or the VDE GS Mark.
For products certified on the basis of harmonized certification agreements.Testing is based on harmonized European standards listed in the ENEC Agreement. Products (at present luminaires and related components, energy saving lamps, IT equipment, transformers, switches for appliances, electrical controls, certain types of capacitors and EMI suppression components) tested to tested to the listed standards may be marked with the ENEC Mark of the VDE. The approval of any other body participating in the ENEC Agreement is not required.
For appliances in compliance with standards for electromagnetic compatibility.The VDE EMC Mark expresses the conformity of a product with applicable standards for electromagnetic compatibility. The reliable function of the product in its electromagnetic environment is also included. The requirements for granting this mark comprise automatically and without restriction the compliance with applicable standards.
For cables, insulated cords, installation conduits and ducts, the VDE Cable Mark is applicable.

For cables and cords, the VDE Identification Thread may be used.
VDE-HARmonization Marking

The VDE HARmonization Marking or VDE HARmonization Thread resp. for cables and insulated cords according to harmonized certification procedures.Testing is based on the Harmonization Documents (HD) listed in the HAR Agreement. Products (harmonized power cables) tested and found in compliance with with the requirements of the mentioned standards may be marked with the VDE HARmonization Marking. Further information is available from the Laboratory for Cables and Cords, Materials and Special Tests.
The VDE Component Mark may be used for electronic components.
The CECC Mark for electronic components according to CECC Specifications.For electronic components according to CECC Specifications (CECC: CENELEC Electronic Components Committee) the CECC Mark may be used.
VDE-Reg.-Nr. XXXXX
VDE-Reg.-Nr. (VDE Certificate of Conformity in conjunction with factory surveillance)This mark is used in two cases: firstly, for products in compliance with applicable clauses of VDE standards in the absence of a fully applicable VDE standard, and secondly, if a product, e.g. a sub-assembly, requires the fulfillment of additional conditions when incorporated into complete equipment. For cables and insulated cords, the VDE-Reg.-Nr. or the relevant mark resp. is applicable in absence of special regulations for products which were tested on the basis other standards. Special constructions and all variations of non-harmonized cables and insulated cords belong to this category of products.

Standard Resistors Values

Sun, 01 Mar 1998 00:00:00 +0000

Reference and Sources:
Manuale di elettronica e telecomunicazioni - Giuseppe Biondo, Enrico Sacchi. Vol.II - IX-40
http://users.eecs.ukans.edu/~kuku/Standard_Resistors.php
The technical specifications for a resistor are:
nominal resistance value [Ohm]
tolerance [%] (indicate the maximum difference (+/-) between nominal and real resistance value)
nominal dissipable power [W]
power-temperature diagrams
temperature coefficient
nominal maximum voltage [V]
noise tension
tension coefficient
resistance-frequency characteristic
the first three are always indicated.
The succession of nominal resistance values fit a geometric progression:
N = 10^((n-1)/k)
where: N is the nominal resistance value at n position;
k is a coefficient related to tolerance in this way:
Tolerance [%] k Series Name
20 6 E6
10 12 E12
5 24 E24
2 48 E48
1 96 E96
0.5 192 E192
0.25 192 E192
0.1 192 E192

Stripline Impedance

Sun, 01 Mar 1998 00:00:00 +0000

This guide was written by Nathan Towne (2009-09)

Introduction

There are quite a few calculators for microstrip and stripline, and commercial products that do the same. But I was looking for a method of constructing a balun of controlled and fairly low impedances, which requires broadside-coupled stripline, where the widths of the traces mostly control the even (common-mode) impedance, and the spacing the odd (differential) impedance. I had in mind using copper tape for the traces and ground planes, polystyrene sheets for dielectric between the traces and the ground plane, and polyethylene or polystyrene sheets setting the spacing between the traces. The problem I encountered is the apparent dearth of information on the impedances of broadside-coupled stripline.

The Ultimate Memory Guide v.6

Sun, 01 Mar 1998 00:00:00 +0000

0. Introduction to Static Electricity

Sun, 01 Mar 1998 00:00:00 +0000

Next page >>
Introduction to Static Electricity
In ordinary circumstances, static electricity and ESD are little more than an annoyance. However, in an increasingly technological age, the familiar static shock we receive when walking across a carpet can be costly or dangerous.
This same static discharge can ignite flammable mixtures and damage electronic components. Static electricity can attract contaminants in clean environments or cause products to stick together.
The cost of ESD-damaged electronic devices alone ranges from only a few cents for a simple diode to several hundred dollars for complex hybrids. Loss of production time in web processing industries due to static attraction is significant. When associated costs of repair and rework, shipping, labor, and overhead are included, clearly the opportunities exist for significant improvements in reducing losses to ESD and static electricity.

0. Table of Contents

Sun, 01 Mar 1998 00:00:00 +0000

This is an original HTML version of THE ULTIMATE MEMORY GUIDE^TM reproduced by permission. ©2000 Kingston Technology Company, Inc. All rights reserved. All trademarks and registered trademarks are the property of their respective owners. PowerPC is a trademark of International Business Machines Corporation, used under license therefrom. Windows is a trademark of Microsoft Corporation. All other trademarks and registered trademarks are the property of their respective owners. This publication may contain typographical errors or technical inaccuracies. Any errors will be periodically corrected in future updates of this publication. Kingston Technology reserves the right to make changes to text and/or illustrations in this document at any time. This publication is the sole property of Kingston Technology and may not be copied or modified in part or in whole without the express permission of Kingston Technology.
TOC Next page >>

00. About the Author

Sun, 01 Mar 1998 00:00:00 +0000

INDEX
About the Author

A versatile inventor, researcher and writer, Mr. Isidor Buchmann is the president, founder and CEO of Cadex Electronics Inc., located in Richmond (Vancouver), Canada.

Fascinated by electronics during his high school years, Mr. Buchmann took to inventing at an early age, designing a fuel-powered engine that was based on continuous combustion. His drawings and theory of operation were reviewed by Felix Wankel, inventor of the Wankel Rotary Engine, who kindly replied that while the design was indeed unique and original, manufacturing would be too expensive to be commercially viable. Further to his credit, Mr. Buchmann invented a broadcast radio that ran on no power — it required only an antenna and a ground connection (it didn’t even use a battery). Mr. Buchmann sold several of these radio receivers to his family and colleagues and later set up a workshop in the attic where he restored and resold old radios. After high school, a four-year apprenticeship as a Radio Technician brought him practical experience in a workshop environment as well as academic theory. Finally, his experience with radio communications in the Swiss army led to his decision to make electronics his life's work.

00. Author's Note

Sun, 01 Mar 1998 00:00:00 +0000

<< Previous page INDEX Next page >>
Author's Note

Battery user groups have asked me to write an edited version of Batteries in a Portable World. The first edition was published in 1997. Much has changed since then.

My very first publication in book form was entitled Strengthening the Weakest Link. It was, in part, a collection of battery articles which I had written. These articles had been published in various trade magazines and gained the interest of many readers. This goes back to the late 1980s and the material covered topics such as the memory effect of NiCd batteries and how to restore them.

00. Frequently Asked Questions about Batteries (FAQ)

Sun, 01 Mar 1998 00:00:00 +0000

INDEX
Frequently Asked Questions about Batteries (FAQ)

INDEX

00. Order Batteries in a Portable World

Sun, 01 Mar 1998 00:00:00 +0000

INDEX
Order Batteries in a Portable World

A paperback book of Batteries in a Portable World can be purchased on this site.

The 300-page book is easy and entertaining to read; it makes minimal use of technical jargon.

The well-organized layout helps you find information quickly. The book is
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understanding this marvelous power source, the battery.

00. Part Four – Beyond Batteries

Sun, 01 Mar 1998 00:00:00 +0000

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Part Four – Beyond Batteries
Chapter 18: Beginnings and Horizons
18.1 About the Author
18.2 About Cadex
18.3 Working with Natural Beauty
18.4 Customer Comments
18.5 Cadex Products
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00. Part One - Battery Basics Everyone Should Know

Sun, 01 Mar 1998 00:00:00 +0000

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Part One - Battery Basics Everyone Should Know
Author's Note

Introduction

Chapter 1: When was the battery invented?

Chapter 2: Battery Chemistries
2.1 Chemistry Comparison
2.2 The Nickel Cadmium (NiCd) Battery
2.3 The Nickel-Metal Hydride (NiMH) Battery
2.4 The Lead Acid Battery
2.5 The Lithium Ion Battery
2.6 The Lithium Polymer Battery
2.7 Reusable Alkaline Batteries
2.8 The Supercapacitor

Chapter 3: The Battery Pack
3.1 The Cylindrical Cell
3.2 The Button Cell
3.3 The prismatic Cell
3.4 The Pouch Cell
3.5 Series and Parallel Configurations
3.6 Protection Circuits

Chapter 4: Proper Charge Methods
4.1 All About Chargers
4.2 Charging the Nickel Cadmium Battery
4.3 Charging the Nickel-Metal Hydride Battery
4.4 Charging the Lead Acid Battery
4.5 Charging the Lithium Ion Battery
4.6 Charging the Lithium Polymer Battery
4.7 Charging at High and Low Temperatures
4.8 Ultra-fast Chargers
4.9 Charge IC Chips

Chapter 5: Discharge Methods
5.1 C-rate
5.2 Depth of Discharge
5.3 Pulse Discharge
5.4 Discharging at High and Low Temperature

00. Part Three – Knowing Your Battery

Sun, 01 Mar 1998 00:00:00 +0000

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Part Three – Knowing Your Battery
Chapter 14: Non-Correctable Battery Problems
14.1 High Self-discharge
14.2 Low Capacity Cells
14.3 Cell Mismatch
14.4 Shorted Cells Loss of Electrolyte

Chapter 15: Caring for Your Batteries from Birth to Retirement
15.1 Storage
15.2 Priming
15.3 The Million Dollar Battery Problem
15.4 To the Service Counter, and No Further
15.5 The Quick Fix
15.6 Battery Warranty
15.7 Battery Recycling

Chapter 16: Practical Battery Tips
16.1 Personal Field Observations
16.2 The Correct Battery for the Job
16.3 Battery Analyzers for Critical Missions

Chapter 17: Did you know . . . ?
17.1 The Cost of Mobile Power
17.2 The Fuel Cell
17.3 The Electric Vehicle
17.4 Strengthening the Weakest Link

00. Part Two – You and the Battery

Sun, 01 Mar 1998 00:00:00 +0000

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Part Two – You and the Battery
Chapter 6: The Secrets of Battery Runtime
6.1 Declining Capacity
6.2 Increasing Internal Resistance
6.3 Elevated Self-Discharge
6.4 Premature Voltage Cut-off

Chapter 7: The ‘Smart’ Battery
7.1 The Single Wire Bus
7.2 The SMBus
7.3 The State-of-Charge Indicator
7.4 The Tri-State Fuel Gauge
7.5 The Target Capacity Selector
7.6 Fuel Gauges for Large Batteries

Chapter 8: Choosing the Right Battery
8.1 What’s the best battery for mobile phones?
8.2 What’s the best battery for two-way radios?
8.3 What’s the best battery forlaptops?
8.4 Selecting a Lasting Battery

Chapter 9: Internal Battery Resistance
9.1 Why do seemingly good batteries fail on digital equipment?
9.2 How is the internal battery resistance measured?
9.3 What’s the difference between internal resistance and impedance?

Chapter 10: Getting the Most from your Batteries
10.1 Memory: myth or fact?
10.2 How to Restore and Prolong Nickel-based Batteries
10.3 The Effect of Zapping
10.4 How to Restore and Prolong Sealed Lead Acid Batteries
10.5 How to Prolong Lithium-based Batteries
10.6 Battery Recovery Rate

Chapter 11: Maintaining Fleet Batteries
11.1 The ‘Green Light’ Lies
11.2 Battery Maintenance, a Function of Quality Control
11.3 Battery Maintenance Made Simple
11.4 Battery Maintenance as a Business

Chapter 12: Battery Maintenance Equipment
12.1 Conditioning Chargers
12.2 Battery Analyzers
12.3 Battery Analyzers for Maintenance-Free Batteries
12.4 Battery throughput
12.5 Battery Maintenance Software

Chapter 13: Making Battery Quick-Test Feasible
13.1 Battery Specific Quick Testing
13.2 Three-Point Quick Test
13.3 The Evolving Battery
13.4 The Cadex Quicktest Method
13.5 How does the Cadex Quicktest work?
13.6 Battery Testing and the Internet
13.7 Electrochemical Impedance Spectroscopy

00. Table Of Content

Sun, 01 Mar 1998 00:00:00 +0000

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "The Digital Audio Resampling Home Page", by Julius O. Smith III, Copyright © 2016-05-17 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Next page >>

Table Of Content
What is Bandlimited Interpolation?
Available Software
Theory of Operation
Abstract
Introduction
Theory of Ideal Bandlimited Interpolation
From Theory to Practice
Implementation
Quantization Issues
Choice of Table Size
Choice of Interpolation Resolution
Conclusions
Appendix A: Exact Sinc-Interpolation of Sampled Periodic Signals
Appendix B: Relation between Sinc and Lagrange Interpolation
Bibliography
About this document ...

00. Table Of Content

Sun, 01 Mar 1998 00:00:00 +0000

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

INDEX Next page >>
Table Of Content

Preface

Outline

Introduction to the DFT

The DFT

Mathematics of the DFT

DFT Math Outline

Introduction to Complex Numbers

Factoring a Polynomial with Real Roots

The Quadratic Formula

Complex Roots

The Fundamental Theorem of Algebra

Complex Numbers

The Complex Plane

More Notation and Terminology

Elementary Relationships

Euler's Formula

De Moivre's Theorem

Numerical Tools in Matlab

Numerical Tools in Mathematica

Proof of Euler's Identity

Euler's Theorem

Positive Integer Exponents

Properties of Exponents

The Exponent Zero

Negative Exponents

Rational Exponents

Special Case: The Mth Roots of Unity

Real Exponents

A First Look at Taylor Series

Imaginary Exponents

Derivatives of f(x)=a^x

Back to e

Sidebar on Mathematica

Back to e^(j theta)

Informal Derivation of Taylor Series Expansion

Derivation of Taylor Series Expansion with Remainder

Formal Statement of Taylor's Theorem

The Weierstrass (Polynomial) Approximation Theorem

Further Notes on Differentiability of Audio Signals

Logarithms, Decibels, and Number Systems

Logarithms

Changing the Base

Logarithms of Negative and Imaginary Numbers

Decibels

Properties of DB Scales

Specific DB Scales

DBm Scale

DBV Scale

DB SPL

DB for Display

Dynamic Range

Linear Number Systems for Digital Audio

Pulse Code Modulation (PCM)

Binary Integer Fixed-Point Numbers

One's Complement Fixed-Point Format

Two's Complement Fixed-Point Format

General Formula for Two's-Complement, Integer Fixed-Point Numbers

''Little Endian'' Formula for Two's-Complement, Integer Fixed-Point Numbers

Fractional Binary Fixed-Point Numbers

How Many Bits are Enough for Digital Audio?

When Do We Have to Swap Bytes When Changing Computers?

Logarithmic Number Systems for Digital Audio

Floating-Point Numbers

Logarithmic Fixed-Point Numbers

-Law Companding

Appendix A: Round-Off Error Variance

Appendix B: Electrical Engineering 101

Sinusoids and Exponentials

Sinusoids

Example Sinusoids

Why Sinusoids are Important

In-Phase and Quadrature Sinusoidal Components

Sinusoids at the Same Frequency

Constructive and Destructive Interference of Sinusoids

Exponentials

Why Exponentials are Important

Audio Decay Time ()

Complex Sinusoids

Circular Motion

Projection of Circular Motion

Positive and Negative Frequencies

The Analytic Signal and Hilbert Transform Filters

Generalized Complex Sinusoids

Sampled Sinusoids

Powers of

Why (Generalized) Complex Sinusoids are Important

Comparing Analog and Digital Complex Planes

Mathematica for Selected Plots

Acknowledgement

Geometric Signal Theory

The DFT

Signals as Vectors

An Example Vector View:

Vector Addition

Vector Subtraction

Signal Metrics

Other Norms

The Inner Product

Linearity of the Inner Product

Norm Induced by the Inner Product

Cauchy-Schwarz Inequality

Triangle Inequality

Triangle Difference Inequality

Vector Cosine

Orthogonality

The Pythagorean Theorem in N-Space

Projection

Signal Reconstruction from Projections

An Example of Changing Coordinates in 2D

General Conditions

Gram-Schmidt Orthogonalization

Appendix: Matlab Examples

The Discrete Fourier Transform (DFT) Derived

The DFT Derived

Geometric Series

Orthogonality of Sinusoids

Orthogonality of the DFT Sinusoids

Norm of the DFT Sinusoids

An Orthonormal Sinusoidal Set

The Discrete Fourier Transform (DFT)

Frequencies in the ''Cracks''

Normalized DFT

The Length 2 DFT

Matrix Formulation of the DFT

Matrices

Matrix Multiplication

The DFT Matrix

Matlab Examples

Figure 7.2

Figure 7.3

DFT Matrix

Fourier Theorems for the DFT

The DFT and its Inverse

Notation and Terminology

Modulo Indexing, Periodic Extension

Signal Operators

Flip Operator

Shift Operator

Convolution

Graphical Convolution

Polynomial Multiplication

Multiplication of Decimal Numbers

Correlation

Stretch Operator

Zero Padding

Repeat Operator

Decimation Operator

Alias Operator

Even and Odd Functions

The Fourier Theorems

Linearity

Conjugation and Reversal

Symmetry

Shift Theorem

Linear Phase Terms

Application of the Shift Theorem to FFT Windows

Convolution Theorem

Dual of the Convolution Theorem

Correlation Theorem

Power Theorem

Rayleigh Energy Theorem (Parseval's Theorem)

Stretch Theorem (Repeat Theorem)

Decimation Theorem (Aliasing Theorem)

Zero Padding Theorem

Bandlimited Interpolation in Time

Conclusions

Acknowledgement

Appendix A: Linear Time-Invariant Filters and Convolution

LTI Filters and the Convolution Theorem

Appendix B: Introductory Statistical Signal Processing

Cross-Correlation

Applications of Cross-Correlation

Autocorrelation

Coherence

Appendix C: Mathematica/Matlab Examples

Appendix D: The Similarity Theorem

Example Applications of the DFT

Spectrum Analysis of a Sinusoid: Windowing, Zero-Padding, and the FFT

Example 1: FFT of a Simple Sinusoid

Example 2: FFT of a Not-So-Simple Sinusoid

Example 3: FFT of a Zero-Padded Sinusoid

Example 4: Blackman Window

Example 5: Use of the Blackman Window

Example 6: Hanning-Windowed Complex Sinusoid

Spectral Phase

A Basic Tutorial on Sampling Theory

Introduction

Reconstruction from Samples--Pictorial Version

Reconstruction from Samples--The Math

Aliasing of Sampled Continuous-Time Signals

Shannon's Sampling Theorem

Figuring Out Sampling Theory by Playing Around with Complex Sinusoids

What frequencies are representable by a geometric sequence?

Recovering a Continuous-Time Signal from its Samples

Method 1: Additive Synthesis

Does it Work?

Introduction to Digital Filter Analysis

Motivating Example and Overview

FIR Filters

Convolution Representation

Finiteness

Causal FIR Filters

Transfer Function

Order

The BiQuad Section

Digital Filter Theory Summary

Linearity and Time-Invariance

Difference Equation

Convolution Representation of LTI Filters

Frequency Response

Phase Delay and Group Delay

Bibliography

Index

About this document ...

00. Table Of Content

Sun, 01 Mar 1998 00:00:00 +0000

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Introduction to Digital Filters with Audio Applications", by Julius O. Smith III, Copyright © 2017-11-26 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

INDEX Next page >>
Table Of Content
Positive Real Functions
Relation to Stochastic Processes
Relation to Schur Functions
Relation to functions positive real in the right-half plane
Special cases and examples
Minimum Phase (MP) polynomials in
Conjectured Properties
Introduction to Digital Filter Theory
Linearity and Time-Invariance
Difference Equation
Convolution Representation
Frequency Response
Phase Delay and Group Delay
Vector Space Concepts
Specific Norms
Concavity (Convexity)
Concave Norms
Gradient Descent
Taylor's Theorem
Newton's Method
Maxims of Signal Processing
Index
Bibliography
About this document ...
INDEX Next page >>

00. TOC

Sun, 01 Mar 1998 00:00:00 +0000

Which battery chemistry is best suited for my application?

Chapter 2: Battery Chemistries
Chapter 6: The Secrets of Battery Runtime, Increasing Internal Resistance
Chapter 8: Choosing the Right Battery
Chapter 9: Internal Battery Resistance
Chapter 15: Caring for Your Batteries from Birth to Retirement

Is the lithium polymer superior to other systems?

Chapter 2: Battery Chemistries, The Lithium Polymer Battery

00. Introduction

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Introduction

During the last few decades, rechargeable batteries have made only moderate improvements in terms of higher capacity and smaller size. Compared with the vast advancements in areas such as microelectronics, the lack of progress in battery technology is apparent. Consider a computer memory core of the sixties and compare it with a modern microchip of the same byte count. What once measured a cubic foot now sits in a tiny chip. A comparable size reduction would literally shrink a heavy-duty car battery to the size of a coin. Since batteries are still based on an electrochemical process, a car battery the size of a coin may not be possible using our current techniques.

00. Links

Sun, 01 Mar 1998 00:00:00 +0000

INDEX
Links

General Links

Elsevier Science, Journal of Power Sources

Energizer Battery Home Page

Electrochemistry Refresher

Online battery simulator

Canadian power technologies VRLA information

ThermoAnalystics Inc.

Battery Review

Huret Associates, Inc.

Manufacturers

www.cadex.com

www.polystor.com/technology.php

www.molienergy.com/products.php

www.sanyobatteries.net/NEWprodsIND.html

Table of Contents
Battery FAQ
New Articles
About the Author
Order Book
Links

Next page >> The battery has become our steady travel companion - it helps call a friend; it expands our workplace beyond four walls; and it supports critical missions for people in need.

Performance specifications for batteries and chargers are often based on ideal conditions.

Manufacturers carry out battery tests on brand new equipment within protected environments. In Batteries in a Portable World, Mr. Buchmann observes the battery as used by consumers in everyday life.

The battery handbook addresses the strengths and limitations of the modern battery. It illustrates which battery chemistry is most appropriate for each application. You will learn about charger technology, battery maintenance to prolong battery life and methods to restore weak batteries with a battery analyzer.

Table of Contents

01. Positive Real Functions

Sun, 01 Mar 1998 00:00:00 +0000

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Introduction to Digital Filters with Audio Applications", by Julius O. Smith III, Copyright © 2017-11-26 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Positive Real Functions
Any passive driving-point impedance, such as the impedance of a violin bridge, is positive real. Positive real functions have been studied extensively in the continuous-time case in the context ofnetwork synthesis [Brune 1931,Van Valkenburg 1960]. Very little, however, seems to be available in the discrete time case. The purpose of this home page is to collect some facts about positive real transfer functions for discrete-time linear systems.

01. What is Bandlimited Interpolation?

Sun, 01 Mar 1998 00:00:00 +0000

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "The Digital Audio Resampling Home Page", by Julius O. Smith III, Copyright © 2016-05-17 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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What is Bandlimited Interpolation?
Bandlimited interpolation of discrete-time signals is a basic tool having extensive application in digital signal processing. In general, the problem is to correctly compute signal values at arbitrary continuous times from a set of discrete-time samples of the signal amplitude. In other words, we must be able to interpolate the signal between samples. Since the original signal is always assumed to be bandlimited to half the sampling rate, (otherwisealiasing distortion would occur upon sampling), Shannon's sampling theorem tells us the signal can be exactly and uniquely reconstructed for all time from its samples by bandlimited interpolation.

01. When was the battery invented?

Sun, 01 Mar 1998 00:00:00 +0000

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1. When was the battery invented?

One of the most remarkable and novel discoveries in the last 400 years has been electricity. One may ask, “Has electricity been around that long?” The answer is yes, and perhaps much longer. But the practical use of electricity has only been at our disposal since the mid-to late 1800s, and in a limited way at first. At the world exposition in Paris in 1900, for example, one of the main attractions was an electrically lit bridge over the river Seine.

01. When was the battery invented? 2

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In the same year, Volta released his discovery of a continuous source of electricity to the Royal Society of London. No longer were experiments limited to a brief display of sparks that lasted a fraction of a second. A seemingly endless stream of electric current was now available.

France was one of the first nations to officially recognize Volta’s discoveries. At the time, France was approaching the height of scientific advancements and new ideas were welcomed with open arms to support the political agenda. By invitation, Volta addressed the Institute of France in a series of lectures at which Napoleon Bonaparte was present as a member of the Institute.

01. When was the battery invented? 3

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Toward the end of the 1800s, giant generators and transformers were built. Transmission lines were installed and electricity was made available to humanity to produce light, heat and movement. In the early twentieth century, the use of electricity was further refined. The invention of the vacuum tube enabled generating controlled signals, amplifications and sound. Soon thereafter, radio was invented, which made wireless communication possible.

02. Available Software

Sun, 01 Mar 1998 00:00:00 +0000

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "The Digital Audio Resampling Home Page", by Julius O. Smith III, Copyright © 2016-05-17 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Available Software
resample-1.5.tar.gz(51 Kbytes) (v1.5 released on 10/07/99)
The resample software package contains free sampling-rate conversion and filter design utilities written in C, including a stand-alone command-line sampling-rate conversion utility called resample. The package compiles readily under Linux and most other UNIX operating systems.
README file for resample software package
sndlib-7 (required)
Older Version for NeXT Computers (49 Kbytes)
Open Source Audio Library Project (OSALP)
OSALP contains a C++ class (GNU LGPL) based on the above resample software.

02. Battery Chemistries

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2. Battery Chemistries

Battery novices often argue that advanced battery systems are now available that offer very high energy densities, deliver 1000 charge/discharge cycles and are paper thin. These attributes are indeed achievable — unfortunately not in the same battery pack. A given battery may be designed for small size and long runtime, but this pack would have a limited cycle life. Another battery may be built for durability, but it would be big and bulky. A third pack may have high energy density and long durability, but would be too expensive for the commercial consumer.

02. Battery Chemistries

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2.8 The Supercapacitor

The supercapacitor resembles a regular capacitor with the exception that it offers very high capacitance in a small size. Energy storage is by means of static charge. Applying a voltage differential on the positive and negative plates charges the supercapacitor. This concept is similar to an electrical charge that builds up when walking on a carpet. Touching an object at ground potential releases the energy. The supercapacitor concept has been around for a number of years and has found many niche applications.

02. Battery Chemistries 2

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2.1 Chemistry Comparison

Let's examine the advantages and limitations of today’s popular battery systems. Batteries are scrutinized not only in terms of energy density but service life, load characteristics, maintenance requirements, self-discharge and operational costs. Since NiCd remains a standard against which other batteries are compared, let’s evaluate alternative chemistries against this classic battery type.

Nickel Cadmium (NiCd) — mature and well understood but relatively low in energy density. The NiCd is used where long life, high discharge rate and economical price are important. Main applications are two-way radios, biomedical equipment, professional video cameras and power tools. The NiCd contains toxic metals and is not environmentally friendly.

02. Battery Chemistries 3

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2.2 The Nickel Cadmium (NiCd) Battery

Alkaline nickel battery technology originated in 1899, when Waldmar Jungner invented the NiCd battery. The materials were expensive compared to other battery types available at the time and its use was limited to special applications. In 1932, the active materials were deposited inside a porous nickel-plated electrode and in 1947, research began on a sealed NiCd battery, which recombined the internal gases generated during charge rather than venting them. These advances led to the modern sealed NiCd battery, which is in use today.

02. Battery Chemistries 4

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2.3 The Nickel-Metal Hydride (NiMH) Battery

Research of the NiMH system started in the 1970s as a means of discovering how to store hydrogen for the nickel hydrogen battery. Today, nickel hydrogen batteries are mainly used for satellite applications. They are bulky, contain high-pressure steel canisters and cost thousands of dollars each. In the early experimental days of the NiMH battery, the metal hydride alloys were unstable in the cell environment and the desired performance characteristics could not be achieved. As a result, the development of the NiMH slowed down. New hydride alloys were developed in the 1980s that were stable enough for use in a cell. Since the late 1980s, NiMH has steadily improved, mainly in terms of energy density. The success of the NiMH has been driven by its high energy density and the use of environmentally friendly metals. The modern NiMH offers up to 40 percent higher energy density compared to NiCd. There is potential for yet higher capacities, but not without some negative side effects. Both NiMH and NiCd are affected by high self-discharge. The NiCd loses about 10 percent of its capacity within the first 24 hours, after which the self-discharge settles to about 10 percent per month. The self-discharge of the NiMH is about one-and-a-half to two times greater compared to NiCd. Selection of hydride materials that improve hydrogen bonding and reduce corrosion of the alloy constituents reduces the rate of self-discharge, but at the cost of lower energy density. The NiMH has been replacing the NiCd in markets such as wireless communications and mobile computing. In many parts of the world, the buyer is encouraged to use NiMH rather than NiCd batteries. This is due to environmental concerns about careless disposal of the spent battery. The question is often asked, “Has NiMH improved over the last few years?” Experts agree that considerable improvements have been achieved, but the limitations remain. Most of the shortcomings are native to the nickel-based technology and are shared with the NiCd battery. It is widely accepted that NiMH is an interim step to lithium battery technology. Initially more expensive than the NiCd, the price of the NiMH has dropped and is now almost at par value. This was made possible with high volume production. With a lower demand for NiCd, there will be a tendency for the price to increase. <table border="0" cellspacing="0" cellpadding="3"> <tr> <td width="482" colspan="2" valign="top"> <table width="100%" border="0" cellspacing="0" cellpadding="0" bgcolor="#000000"> <tr> <td></td> </tr> </table> </td> </tr> <tr> <td width="482" colspan="2" valign="top" bgcolor="#E6E6E6"> Advantages and Limitations of NiMH Batteries </td> </tr> <tr> <td width="482" colspan="2" valign="top"> <table width="100%" border="0" cellspacing="0" cellpadding="0" bgcolor="#000000"> <tr> <td></td> </tr> </table> </td> </tr> <tr> <td width="65" valign="top"> Advantages </td> <td width="417" valign="top"> 30 – 40 percent higher capacity over a standard NiCd. The NiMH has potential for yet higher energy densities. Less prone to memory than the NiCd. Periodic exercise cycles are required less often. Simple storage and transportation — transportation conditions are not subject to regulatory control. Environmentally friendly — contains only mild toxins; profitable for recycling. </td> </tr> <tr> <td width="65" valign="top" bgcolor="#F3F3F3"> Limitations </td> <td width="417" valign="top" bgcolor="#F3F3F3"> Limited service life — if repeatedly deep cycled, especially at high load currents, the performance starts to deteriorate after 200 to 300 cycles. Shallow rather than deep discharge cycles are preferred. Limited discharge current — although a NiMH battery is capable of delivering high discharge currents, repeated discharges with high load currents reduces the battery’s cycle life. Best results are achieved with load currents of 0.2C to 0.5C (one-fifth to one-half of the rated capacity). More complex charge algorithm needed — the NiMH generates more heat during charge and requires a longer charge time than the NiCd. The trickle charge is critical and must be controlled carefully. High self-discharge — the NiMH has about 50 percent higher self-discharge compared to the NiCd. New chemical additives improve the self-discharge but at the expense of lower energy density. Performance degrades if stored at elevated temperatures — the NiMH should be stored in a cool place and at a state-of-charge of about 40 percent. High maintenance — battery requires regular full discharge to prevent crystalline formation. About 20 percent more expensive than NiCd — NiMH batteries designed for high current draw are more expensive than the regular version. </td> </tr> <tr valign="middle"> <td colspan="2" height="18"> <table width="100%" border="0" cellspacing="0" cellpadding="0" bgcolor="#000000"> <tr> <td></td> </tr> </table> </td> </tr> </table> <a name="_Toc507815236">Figure 2-</a>3:       Advantages and limitations of NiMH batteries</blockquote><a href="/guides/electronics/bpw/c02_03"><< Previous page</a>  <a href="/guides/electronics/bpw/00_toc">INDEX</a>  <a href="/guides/electronics/bpw/c02_05">Next page >></a>

02. Battery Chemistries 5

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2.4 The Lead Acid Battery

Invented by the French physician Gaston Planté in 1859, lead acid was the first rechargeable battery for commercial use. Today, the flooded lead acid battery is used in automobiles, forklifts and large uninterruptible power supply (UPS) systems.

During the mid 1970s, researchers developed a maintenance-free lead acid battery, which could operate in any position. The liquid electrolyte was transformed into moistened separators and the enclosure was sealed. Safety valves were added to allow venting of gas during charge and discharge.

02. Battery Chemistries 6

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2.5 The Lithium Ion Battery

Pioneer work with the lithium battery began in 1912 under G.N. Lewis but it was not until the early 1970s that the first non-rechargeable lithium batteries became commercially available. Attempts to develop rechargeable lithium batteries followed in the 1980s, but failed due to safety problems.

Lithium is the lightest of all metals, has the greatest electrochemical potential and provides the largest energy density per weight. Rechargeable batteries using lithium metal anodes (negative electrodes) are capable of providing both high voltage and excellent capacity, resulting in an extraordinary high energy density.

02. Battery Chemistries 7

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As a trade-off, spinel offers a slightly lower energy density, suffers capacity loss at temperatures above 40°C and ages quicker than cobalt. Figure 2-6 compares the advantages and disadvantages of the two chemistries.

Cobalt Manganese (Spinel)

Energy density (Wh/kg) 140 ¹ 120 ¹

Safety On overcharge, the cobalt electrode provides extra lithium, which can form into metallic lithium, causing a potential safety risk if not protected by a safety circuit. On overcharge, the manganese electrode runs out of lithium causing the cell only to get warm. Safety circuits can be eliminated for small 1 and 2 cell packs.

Temperature Wide temperature range. Best suited for operation at elevated temperature. Capacity loss above +40°C. Not as durable at higher temperatures.

Aging Short-term storage possible. Impedance increases with age. Newer versions offer longer storage. Slightly less than cobalt. Impedance changes little over the life of the cell. Due to continuous improvements, storage time is difficult to predict.

Life Expectancy 300 cycles, 50% capacity at 500 cycles. May be shorter than cobalt.

Cost Raw material relatively high; protection circuit adds to costs. Raw material 30% lower than cobalt. Cost advantage on simplified protection circuit.

Figure 2-6: Comparison of cobalt and manganese as positive electrodes.
Manganese is inherently safer and more forgiving if abused but offers a slightly lower energy density. Manganese suffers capacity loss at temperature above 40°C and ages quicker than cobalt.

02. Battery Chemistries 8

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2.6 The Lithium Polymer Battery

The Li-polymer differentiates itself from other battery systems in the type of electrolyte used. The original design, dating back to the 1970s, uses a dry solid polymer electrolyte only. This electrolyte resembles a plastic-like film that does not conduct electricity but allows an exchange of ions (electrically charged atoms or groups of atoms). The polymer electrolyte replaces the traditional porous separator, which is soaked with electrolyte.

02. Battery Chemistries 9

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2.7 Reusable Alkaline Batteries

The idea of recharging alkaline batteries is not new. Although not endorsed by manufacturers, ordinary alkaline batteries have been recharged in households for many years. Recharging these batteries is only effective, however, if the cells have been discharged to less than 50 percent of their total capacity. The number of recharges depends solely on the depth of discharge and is limited to a few at best. With each recharge, less capacity can be reclaimed. There is a cautionary advisory, however: charging ordinary alkaline batteries may generate hydrogen gas, which can lead to explosion. It is therefore not prudent to charge ordinary alkaline unsupervised.

02. Relation to Stochastic Processes

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Relation to Stochastic Processes
Theorem. If a stationary random process has a rational power spectral density corresponding to an autocorrelation function , then

03. Relation to Schur Functions

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Relation to Schur Functions
Definition. A Schur function is defined as a complex function analytic and of modulus not exceeding unity in .
Theorem. The function

03. The Battery Pack

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3. The Battery Pack

In the 1700 and 1800s, cells were encased in glass jars. Later, larger batteries were developed that used wooden containers. The inside was treated with a sealant to prevent electrolyte leakage. With the need for portability, the cylindrical cell appeared. After World War II, these cells became the standard format for smaller, rechargeable batteries.

Downsizing required smaller and more compact cell design. The button cell, which gained popularity in the 1980s, was a first attempt to achieve a reasonably flat geometry, or obtain higher voltages in a compact profile by stacking. The early 1990s brought the prismatic cell, which was followed by the modern pouch cell.

03. The Battery Pack 2

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3.2 The Button Cell

The button cell was developed to miniaturize battery packs and solve stacking problems. Today, this architecture is limited to a small niche market. Non-rechargeable versions of the button cell continue to be popular and can be found in watches, hearing aids and memory backup.

The main applications of the rechargeable button cell are (or were) older cordless telephones, biomedical devices and industrial instruments. Although small in design and inexpensive to manufacture, the main drawback is swelling if charged too rapidly. Button cells have no safety vent and can only be charged at a 10 to 16 hour charge rate. New designs claim rapid charge capability.

03. The Battery Pack 3

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3.4 The Pouch Cell

Cell design made a profound advance in 1995 when the pouch cell concept was developed. Rather than using an expensive metallic cylinder and glass-to-metal electrical feed-through to insulate the opposite polarity, the positive and negative plates are enclosed in flexible, heat-sealable foils. The electrical contacts consist of conductive foil tabs that are welded to the electrode and sealed to the pouch material. Figure 3-4 illustrates the pouch cell.

03. The Battery Pack 4

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3.5 Series and Parallel Configurations

In most cases, a single cell does not provide a high enough voltage and a serial connection of several cells is needed. The metallic skin of the cell is insulated to prevent the ‘hot’ metal cylinders from creating an electrical short circuit against the neighboring cell.

Nickel-based cells provide a nominal cell voltage of 1.25V. A lead acid cell delivers 2V and most Li-ion cells are rated at 3.6V. The spinel (manganese) and Li-ion polymer systems sometimes use 3.7V as the designated cell voltage. This is the reason for the often unfamiliar voltages, such as 11.1V for a three cell pack of spinel chemistry.

03. The Battery Pack 5

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3.6 Protection Circuits

Most battery packs include some type of protection to safeguard battery and equipment, should a malfunction occur. The most basic protection is a fuse that opens if excessively high current is drawn. Some fuses open permanently and render the battery useless once the filament is broken; other fuses are based on a Polyswitch™, which resembles a resettable fuse. On excess current, the Polyswitch™ creates a high resistance, inhibiting the current flow. When the condition normalizes, the resistance of the switch reverts to the low ON position, allowing normal operation to resume. Solid-state switches are also used to disrupt the current. Both solid-state switches and the Polyswitch™ have a residual resistance to the ON position during normal operation, causing a slight increase in internal battery resistance.

03. The Battery Pack 6

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Each parallel string of cells of a Li-ion pack needs independent voltage monitoring. The more cells that are connected in series, the more complex the protection circuit becomes. Four cells in series is the practical limit for commercial applications.

The internal protection circuit of a mobile phone while in the ON position has a resistance of 50 to 100 mW. The circuit normally consists of two switches connected in series. One is responsible for high cut-off, the other for low cut-off. The combined resistance of these two devices virtually doubles the internal resistance of a battery pack, especially if only one cell is used. Battery packs powering mobile phones, for example, must be capable of delivering high current bursts. The internal protection does, in a certain way, interfere with the current delivery.

03. Theory of Operation

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Theory of Operation

Subsections
Abstract
Introduction
Theory of Ideal Bandlimited Interpolation
From Theory to Practice
Implementation
Quantization Issues
Choice of Table Size
Choice of Interpolation Resolution
Conclusions
Appendix A: Exact Sinc-Interpolation of Sampled Periodic Signals
Appendix B: Relation between Sinc and Lagrange Interpolation

04. Abstract

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Abstract
This tutorial describes a technique for bandlimited interpolation of discrete-time signals which supports signal evaluation at an ``arbitrary'' time, and which performs well for smoothly changing sampling rates, such as needed for digital audio ``scrubbing.'' The method is based on interpolated look-up in a table of filter coefficients, so as to make the filter impulse response available effectively in continuous-time form. A single pre-computed filter table handles all interpolation times and sampling-rate conversion ratios. Formulas are given for determining the look-up table size needed for a given precision requirement. This tutorial is an expansion of the conference paper [Smith and Gossett 1984].

04. Proper Charge Methods

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4. Proper Charge Methods

To a large extent, the performance and longevity of rechargeable batteries depends on the quality of the chargers. Battery chargers are commonly given low priority, especially on consumer products. Choosing a quality charger makes sense. This is especially true when considering the high cost of battery replacements and the frustration that poorly performing batteries create. In most cases, the extra money invested is returned because the batteries last longer and perform more efficiently.

04. Proper Charge Methods 10

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4.8 Ultra-fast Chargers

Some charger manufacturers claim amazingly short charge times of 30 minutes or less. With well-balanced cells and operating at moderate room temperatures, NiCd batteries designed for fast charging can indeed be charged in a very short time. This is done by simply dumping in a high charge current during the first 70 percent of the charge cycle. Some NiCd batteries can take as much a 10C, or ten times the rated current. Precise SoC detection and temperature monitoring are essential.

04. Proper Charge Methods 2

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There are three types of chargers for nickel-based batteries. They are:

Slow Charger — Also known as ‘overnight charger’ or ‘normal charger’, the slow-charger applies a fixed charge rate of about 0.1C (one tenth of the rated capacity) for as long as the battery is connected. Typical charge time is 14 to 16 hours. In most cases, no full-charge detection occurs to switch the battery to a lower charge rate at the end of the charge cycle. The slow-charger is inexpensive and can be used for NiCd batteries only. With the need to service both NiCd and NiMH, these chargers are being replaced with more advanced units.

04. Proper Charge Methods 3

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Simple Guidelines

A charger designed to service NiMH batteries can also accommodate NiCd’s, but not the other way around. A charger only made for the NiCd batteries could overcharge the NiMH battery.

While many charge methods exist for nickel-based batteries, chargers for lithium-based batteries are more defined in terms of charge method and charge time. This is, in part, due to the tight charge regime and voltage requirements demanded by these batteries. There is only one way to charge Li-ion/Polymer batteries and the so-called ‘miracle chargers’, which claim to restore and prolong battery life, do not exist for these chemistries. Neither does a super-fast charging solution apply.

04. Proper Charge Methods 4

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More advanced NiCd chargers sense the rate of temperature increase, defined as dT/dt, or the change in temperature over charge time, rather than responding to an absolute temperature (dT/dt is defined as delta Temperature / delta time). This type of charger is kinder to the batteries than a fixed temperature cut-off, but the cells still need to generate heat to trigger detection. To terminate the charge, a temperature increase of 1°C (1.8°F) per minute with an absolute temperature cut-off of 60°C (140°F) works well. Because of the relatively large mass of a cell and the sluggish propagation of heat, the delta temperature, as this method is called, will also enter a brief overcharge condition before the full-charge is detected. The dT/dt method only works with fast chargers.

04. Proper Charge Methods 5

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4.3 Charging the Nickel-Metal Hydride Battery

Chargers for NiMH batteries are very similar to those of the NiCd system but the electronics is generally more complex. To begin with, the NiMH produces a very small voltage drop at full charge. This NDV is almost non-existent at charge rates below 0.5C and elevated temperatures. Aging and cell mismatch works further against the already minute voltage delta. The cell mismatch gets worse with age and increased cycle count, which makes the use of the NDV increasingly more difficult.

04. Proper Charge Methods 6

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4.4 Charging the Lead Acid Battery

The charge algorithm for lead acid batteries differs from nickel-based chemistry in that voltage limiting rather than current limiting is used. Charge time of a sealed lead acid (SLA) is 12 to 16 hours. With higher charge currents and multi-stage charge methods, charge time can be reduced to 10 hours or less. SLAs cannot be fully charged as quickly as nickel-based systems.

A multi-stage charger applies constant-current charge, topping charge and float charge (see Figure 4-3). During the constant current charge, the battery charges to 70 percent in about five hours; the remaining 30 percent is completed by the slow topping charge. The topping charge lasts another five hours and is essential for the well-being of the battery. This can be compared to a little rest after a good meal before resuming work. If the battery is not completely saturated, the SLA will eventually lose its ability to accept a full charge and the performance of the battery is reduced. The third stage is the float charge, which compensates for the self-discharge after the battery has been fully charged.

04. Proper Charge Methods 7

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Plastic SLA batteries arriving from vendors with less than 2.10V per cell are rejected by some buyers who inspect the battery during quality control. Low voltage suggests that the battery may have a soft short, a defect that cannot be corrected with cycling. Although cycling may increase the capacity of these batteries, the extra cycles compromise the service life of the battery. Furthermore, the time and equipment required to make the battery fully functional adds to operational costs.

04. Proper Charge Methods 8

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4.5 Charging the Lithium Ion Battery

The Li-ion charger is a voltage-limiting device similar to the lead acid battery charger. The difference lies in a higher voltage per cell, tighter voltage tolerance and the absence of trickle or float charge when full charge is reached.

While the lead acid battery offers some flexibility in terms of voltage cut-off, manufacturers of Li-ion cells are very strict on setting the correct voltage. When the Li- ion was first introduced, the graphite system demanded a charge voltage limit of 4.10V/cell. Although higher voltages deliver increased energy densities, cell oxidation severely limited the service life in the early graphite cells that were charged above the 4.10V/cell threshold. This effect has been solved with chemical additives. Most commercial Li-ion cells can now be charged to 4.20V. The tolerance on all Li-ion batteries is a tight +/-0.05V/cell.

04. Proper Charge Methods 9

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4.6 Charging the Lithium Polymer Battery

The charge process of a Li-Polymer is similar to that of the Li-ion. Li-Polymer uses dry electrolyte and takes 3 to 5 hours to charge. Li-ion polymer with gelled electrolyte, on the other hand, is almost identical to that of Li-ion. In fact, the same charge algorithm can be applied. With most chargers, the user does not need to know whether the battery being charged is Li-ion or Li-ion polymer.

04. Relation to functions positive real in the right-half plane

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Relation to functions positive real in the right-half plane
Theorem. , where is any positive real number.

05. Discharge Methods

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5. Discharge Methods

The purpose of a battery is to store energy and release it at the appropriate time in a controlled manner. Being capable of storing a large amount of energy is one thing; the ability to satisfy the load demands is another. The third criterion is being able to deliver all available energy without leaving precious energy behind when the equipment cuts off.

In this chapter, we examine how different discharge methods can affect the deliverance of power. Further, we look at the load requirements of various portable devices and evaluate the performance of each battery chemistry in terms of discharge.

05. Discharge Methods 2

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5.2 Depth of Discharge

The typical end-of-discharge voltage for nickel-based batteries is 1V/cell. At that voltage level, about 99 percent of the energy is spent and the voltage starts to drop rapidly if the discharge continues. Discharging beyond the cut-off voltage must be avoided, especially under heavy load.

Since the cells in a battery pack cannot be perfectly matched, a negative voltage potential (cell reversal) across a weaker cell occurs if the discharge is allowed to continue beyond the cut-off point. The larger the number of cells connected in series, the greater the likelihood of this occurring.

05. Discharge Methods 3

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The SLA should not be discharged beyond 1.75V per cell, nor can it be stored in a discharged state. The cells of a discharged SLA sulfate, a condition that renders the battery useless if left in that state for a few days.

The Li-ion typically discharges to 3.0V/cell. The spinel and coke versions can be discharged to 2.5V/cell. The lower end-of-discharge voltage gains a few extra percentage points. Since the equipment manufacturers cannot specify which battery type may be used, most equipment is designed for a three-volt cut-off.

05. Discharge Methods 4

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5.3 Pulse Discharge

Battery chemistries react differently to specific loading requirements. Discharge loads range from a low and steady current used in a flashlight, to intermittent high current bursts in a power tool, to sharp current pulses required for digital communications equipment, to a prolonged high current load for an electric vehicle traveling at highway speed. Because batteries are chemical devices that must convert higher-level active materials into an alternate state during discharge, the speed of such transaction determines the load characteristics of a battery. Also referred to as concentration polarization, the nickel and lithium-based batteries are superior to lead-based batteries in reaction speed. This reflects in good load characteristics.

05. Discharge Methods 5

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5.4 Discharging at High and Low Temperature

Batteries function best at room temperature. Operating batteries at an elevated temperature dramatically shortens their life. Although a lead acid battery may deliver the highest capacity at temperatures above 30°C (86°F), prolonged use under such conditions decreases the life of the battery.

Similarly, a Li-ion performs better at high temperatures. Elevated temperatures temporarily counteracts the battery’s internal resistance, which is a result of aging. The energy gain is short-lived because elevated temperature promotes aging by further increasing the internal resistance.

05. Introduction

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Introduction
Bandlimited interpolation of discrete-time signals is a basic tool having extensive application in digital signal processing. In general, the problem is to correctly compute signal values at arbitrary continuous times from a set of discrete-time samples of the signal amplitude. In other words, we must be able to interpolate the signal between samples. Since the original signal is always assumed to be bandlimited to half the sampling rate, (otherwisealiasing distortion would occur upon sampling), Shannon's sampling theorem tells us the signal can be exactly and uniquely reconstructed for all time from its samples by bandlimited interpolation.

05. Special cases and examples

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Special cases and examples
The sum of positive real functions is positive real.
The difference of positive real functions is conditionally positive real.
The product or division of positive real functions is conditionally PR.
PR not PR for .

06. Minimum Phase (MP) polynomials in Z

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Minimum Phase (MP) polynomials in
All properties of MP polynomials apply without modification to marginallystable allpole transfer functions (cf. Thm. (1)).
Every first-order MP polynomial is positive real.

06. The Secrets of Battery Runtime

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6. The Secrets of Battery Runtime

Is the runtime of a portable device directly related to the size of the battery and the energy it can hold? In most cases, the answer is yes. But with digital equipment, the length of time a battery can operate is not necessarily linear to the amount of energy stored in the battery.

In this chapter we examine why the specified runtime of a portable device cannot always be achieved, especially after the battery has aged. We address the four renegades that are affecting the performance of the battery. They are: declining capacity, increasing internal resistance, elevated self-discharge, and premature voltage cut-off on discharge.

06. The Secrets of Battery Runtime 2

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Increasing Internal Resistance

To a large extent, the internal resistance, also known as impedance, determines the performance and runtime of a battery. If measured with an AC signal, the internal resistance of a battery is also referred to as impedance. High internal resistance curtails the flow of energy from the battery to the equipment.

A battery with simulated low and high internal resistance is illustrated below. While a battery with low internal resistance can deliver high current on demand, a battery with high resistance collapses with heavy current. Although the battery may hold sufficient capacity, the voltage drops to the cut-off line and the ‘low battery’ indicator is triggered. The equipment stops functioning and the remaining energy is undelivered.

06. The Secrets of Battery Runtime 3

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6.3 Elevated Self-Discharge

All batteries exhibit a certain amount of self-discharge; the highest is visible on nickel-based batteries. As a rule, a nickel-based battery discharges 10 to 15 percent of its capacity in the first 24 hours after charge, followed by 10 to 15 percent every month thereafter.

The self-discharge on the Li-ion battery is lower compared to the nickel-based systems. The Li-ion self-discharges about five percent in the first 24 hours and one to two percent thereafter. Adding the protection circuit increases the self-discharge to ten percent per month.

06. Theory of Ideal Bandlimited Interpolation

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Theory of Ideal Bandlimited Interpolation
We review briefly the ``analog interpretation'' of sampling rate conversion[Crochiere and Rabiner 1983] on which the present method is based. Suppose we have samples of a continuous absolutely integrable signal , where is time in seconds (real), ranges over the integers, and is the sampling period. We assume is bandlimited to, where is the sampling rate. If denotes the Fourier transform of , i.e., , then we assume for . Consequently, Shannon's sampling theorem gives us that can be uniquely reconstructed from the samples via
(1)

07. Conjectured Properties

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Conjectured Properties
The following conjectures are true for analog positive-real functions, but no rigorous attempt was made to establish them in the discrete-time case.
If all poles and zeros of a PR function are on the unit circle, then they alternate along the circle.

07. From Theory to Practice

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From Theory to Practice
The summation in Eq. (1) cannot be implemented in practice because the ``ideal lowpass filter'' impulse response actually extends from minus infinity to infinity. It is necessary in practice to windowthe ideal impulse response so as to make it finite. This is the basis of the window method for digital filter design[Digital Signal Processing Committee 1979a,Rabiner and Gold 1975]. While many other filter design techniques exist, the window method is simple and robust, especially for very long impulse responses. In the case of the algorithm presented below, the filter impulse response is very long because it is heavily oversampled. Another approach is to design optimal decimated ``sub-phases'' of the filter impulse response, which are then interpolated to provide the ``continuous'' impulse response needed for the algorithm [Putnam and Smith 1997].

07. The ‘Smart’ Battery

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7. The ‘Smart’ Battery

Aspeaker at a battery seminar remarked that, “The battery is a wild animal and artificial intelligence domesticates it.” An ordinary or ‘dumb’ battery has the inherit problem of not being able to display the amount of reserve energy it holds. Neither weight, color, nor size provides any indication of the battery’s state-of-charge (SoC) and state-of-health (SoH). The user is at the mercy of the battery when pulling a freshly charged battery from the charger.

07. The ‘Smart’ Battery 2

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The SMBus

The SMBus is the most complete of all systems. It represents a large effort from the portable electronic industry to standardize to one communications protocol and one set of data. The SMBus is a two-wire interface system through which simple power-related chips can communicate with the rest of the system. One wire handles the data; the second is the clock. It uses I²C as its backbone. Defined by Philips, the I²C is a synchronous multi-drop bi-directional communications system, which operates at a speed of up to 100 kilohertz (kHz).

07. The ‘Smart’ Battery 3

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Architecture — An SMBus battery contains permanent and temporary data. The permanent data is programmed into the battery at the time of manufacturing and include battery ID number, battery type, serial number, manufacturer’s name and date of manufacture. The temporary data is acquired during use and consists of cycle count, user pattern and maintenance requirements. Some of the temporary data is being replaced and renewed during the life of the battery.

07. The ‘Smart’ Battery 4

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Negatives of the SMBus — Like any good invention, the SMBus battery has some serious downsides that must be addressed. For starters, the ‘smart’ battery costs about 25 percent more than the ‘dumb’ equivalent. In addition, the ‘smart’ battery was intended to simplify the charger, but a full-fledged Level 3 charger costs substantially more than a regular dumb model.

A more serious issue is maintenance requirements, better known as capacity re-learning. This procedure is needed on a regular basis to calibrate the battery. The Engineering Manager of Moli Energy, a large Li-ion cell manufacturer commented, “With the Li-ion battery we have eliminated the memory effect, but are we introducing digital memory with the SMBus battery?”

07. The ‘Smart’ Battery 5

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7.3 The State-of-Charge Indicator

Most SMBus batteries are equipped with a charge level indicator. When pressing a SoC button on a battery that is fully charged, all signal lights illuminate. On a partially discharged battery, half the lights illuminate, and on an empty battery, all lights remain dark. Figure 7-4 shows such a fuel gauge.

Figure 7-4: State-of-charge readout of a ‘smart’ battery.
Although the state-of-charge is displayed, the state-of-health and its predicted runtime are unknown.

07. The ‘Smart’ Battery 6

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7.5 The Target Capacity Selector

For users that simply need a go/no go answer and do not want to bother about other battery information, chargers are available that feature a target capacity selector. Adjustable to 60, 70 or 80 percent, the target capacity selector acts as a performance check and flags batteries that do not meet set requirements.

If a battery falls below target, the charger triggers the condition light. The user is prompted to press the condition button to cycle the battery. Condition consists of charge/discharge/charge and performs calibration and conditioning functions. If the battery does not recover after the conditioning service, the fail light illuminates, indicating that the battery should be replaced. A green ready light at the completion of the program assures that the battery meets the required performance level.

07. The ‘Smart’ Battery 7

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7.6 Fuel Gauges for Large Batteries

Most ‘smart’ battery applications today are limited to portable electronic equipment, and the electronic circuit is built right into the battery pack. In applications where larger ‘smart’ batteries are needed, such as electric wheelchairs, scooters, robots and forklifts, the electronic circuit may be placed in a box external to the battery.

The main benefit of adding intelligence to the battery is to enable the measurement of SoH and reserve energy. Most measuring devices used are based on voltage, which is known to be highly inaccurate.

08. Choosing the Right Battery

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8. Choosing the Right Battery

What causes a battery to wear down — is it mechanical or chemical? The answer is ‘both’. A battery is a perishable product that starts deteriorating from the time it leaves the factory. Similar to a spring under tension, a battery seeks to revert to its lowest denominator. The rate of aging is subject to depth of discharge, environmental conditions, charge methods and maintenance procedures (or lack thereof). Each battery chemistry behaves differently in terms of aging and wear through normal use.

08. Choosing the Right Battery 2

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8.2 What’s the best battery for two-way radios?

The two-way radio market uses mostly NiCd batteries. In the last few years, environmental agencies have been attempting to discourage the use of NiCd, especially in Europe. NiMH have been tried and tested in two-way radios for a number of years but the results are mixed. Shorter cycle life compared to NiCd is the major drawback.

The reasons for the relatively short life of NiMH are multi-fold. NiMH is less robust than NiCd and has a cycle life expectancy that is half or one third that of the standard NiCd. In addition, NiMH prefers a moderate discharge current of 0.5C or less. A two-way radio, on the other hand, draws a discharge current of about 1.5A when transmitting at 4W of power. High discharge loads shorten the life of the NiMH battery considerably.

08. Choosing the Right Battery 3

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8.4 Selecting a Lasting Battery

As part of an ongoing research program to find the optimum battery system for selected applications, Cadex has performed life cycle tests on NiCd, NiMH and Li-ion batteries. All tests were carried out on the Cadex 7000 Series battery analyzers in the test labs of Cadex, Vancouver, Canada. The batteries tested received an initial full-charge, and then underwent a regime of continued discharge/charge cycles. The internal resistance was measured with Cadex’s Ohmtest™ method, and the self-discharge was obtained from time-to-time by reading the capacity loss incurred during a 48-hour rest period. The test program involved 53 commercial telecommunications batteries of different models and chemistries. One battery of each chemistry displaying typical behavior was chosen for the charts below.

08. Choosing the Right Battery 4

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The NiMH Battery — Figure 8-3 examines the NiMH, a battery that offers high energy density at reasonably low cost. We observe good performance at first but past the 300-cycle mark, the performance starts to drift downwards rapidly. One can detect a swift increase in internal resistance and self-discharge after cycle count 700.

Figure 8-3: Characteristics of a NiMH battery.
This battery offers good performance at first but past the 300-cycle mark, the capacity, internal resistance and self-discharge start to deteriorate rapidly. This illustrations shows results for a 6V, 950mA NiMH.

08. Implementation

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Implementation
Our implementation provides signal evaluation at an arbitrary time, where time is specified as an unsigned binary fixed-point number in units of the input sampling period (assumed constant). Figure 6 shows the time register , and Figure 7 shows an example configuration of the input signal and lowpass filter at a given time. The time register is divided into three fields: The leftmost field gives the number of samples into the input signal buffer, the middle field is an initial index into the filter coefficient table , and the rightmost field is interpreted as a number between and for doinglinear interpolation between samples and (initially) of the filter table. The concatenation of and are called which is interpreted as the position of the current time between samples and of the input signal.

08. Introduction to Digital Filter Theory

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Introduction to Digital Filter Theory
In this section, linearity, time-invariance and four basic representations of digital filters are defined: thedifference equation coefficients, impulse response, transfer function, and frequency response. Next the concepts ofphase delay, group delay, poles and zeros, and filter stability are defined. This elementary material was taken from course notes for a class given at Stanford by the author in 1979.

09. Internal Battery Resistance

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9. Internal Battery Resistance

With the move from analog to digital devices, new demands are being placed on the battery. Unlike analog equipment that draws a steady current, the digital mobile phone, for example, loads the battery with short, high current bursts.

Increasingly, mobile communication devices are moving from voice only to multimedia which allows sending and receiving data, still pictures and even video. Such transmissions add to the bandwidth, which require several times the battery power compared to voice only.

09. Internal Battery Resistance 2

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9.2 How is the internal battery resistance measured?

A number of techniques are used to measure internal battery resistance. One common method is the DC load test, which applies a discharge current to the battery while measuring the voltage drop. Voltage over current provides the internal resistance (see Figure 9-5).

Figure 9-5: DC load test.
The DC load test measures the battery’s internal resistance by reading the voltage drop. A large drop indicates high resistance.

09. Internal Battery Resistance 3

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Figure 9-8 compares the three methods of measuring the internal resistance of a battery and observe the accuracy. In a good battery, the discrepancies between methods are minimal. The test results deviate to a larger degree on packs with poor SoH.

Impedance measurement alone does not provide a definite conclusion as to the battery performance. The mW readings may vary widely and are dependent on battery chemistry, cell size (mAh rating), type of cell, number of cells connected in series, wiring and contact type.

09. Linearity and Time-Invariance

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Linearity and Time-Invariance
In everyday terms, the fact that a filter islinear means simply that
the amplitude of the output is proportional to the amplitude of the input, and

09. Quantization Issues

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Quantization Issues
In this section, we investigate the requirements on the sampling density of the lowpass-filter impulse response, and the number of bits required in the interpolation factor . These quantities are determined by computing the worst-case error and comparing it to the filter coefficient quantization error.

1. An Introduction to ESD

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1. An Introduction to ESD
History & Background
The decade of the 90's may be remembered as the Decade of Quality in the electronics industry. Increased competition, six-sigma quality, and ISO 9000 have forced a recommitment to quality even in those companies that might not have done so willingly. As we examine our environments for quality improvement areas, electrostatic discharge (ESD) remains a key target.
Static electricity has been an industrial problem for centuries. As early as the 1400’s, European and Caribbean forts were using static control procedures and devices to prevent electrostatic discharge ignition of black powder stores. By the 1860's, paper mills throughout the U.S. employed basic grounding, flame ionization techniques, and steam drums to dissipate static electricity from the paper web as it traveled through the drying process. The age of electronics brought with it new problems associated with static electricity and electrostatic discharge. And, as electronic devices became faster and smaller, their sensitivity to ESD increased.

1. WHAT IS MEMORY?

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1. WHAT IS MEMORY?
1.1. INTRODUCTION
1.2. THE ROLE OF MEMORY IN THE COMPUTER
1.3. THE DIFFERENCE BETWEEN MEMORY AND STORAGE
1.4. MEMORY AND PERFORMANCE
1.5. HOW MUCH MEMORY DO YOU NEED?
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1.1. INTRODUCTION

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1.1. INTRODUCTION
These days, no matter how much memory your computer has, it never seems to be quite enough. Not long ago, it was unheard of for a PC (Personal Computer), to have more than 1 or 2 MB (Megabytes) of memory. Today, most systems require 64MB to run basic applications. And up to 256MB or more is needed for optimal performance when using graphical and multimedia programs.

As an indication of how much things have changed over the past two decades, consider this: in 1981, referring to computer memory, Bill Gates said, “640K (roughly 1/2 of a megabyte) ought to be enough for anybody.”

For some, the memory equation is simple: more is good; less is bad. However, for those who want to know more, this reference guide contains answers to the most common questions, plus much, much more.

1.2. THE ROLE OF MEMORY IN THE COMPUTER

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1.2. THE ROLE OF MEMORY IN THE COMPUTER
People in the computer industry commonly use the term “memory” to refer to RAM (Random Access Memory). A computer uses RAM to hold temporary instructions and data needed to complete tasks. This enables the computer’s CPU (Central Processing Unit), to access instructions and data stored in memory very quickly.

A good example of this is when the CPU loads an application program – such as a word processing or page layout program – into memory, thereby allowing the application program to work as quickly and efficiently as possible. In practical terms, having the program loaded into memory means you can get work done more quickly with less time spent waiting for the computer to perform tasks.

The process begins when you enter a command from your keyboard. The CPU interprets the command and instructs the hard drive to load the command or prgram into memory. Once the data is loaded into memory, the CPU is able to access it much more quickly than if it had to retrieve it from the hard drive.

This process of putting things the CPU needs in a place where it can get at them more quickly is similar to placing various electronic files and documents you’re using on the computer into a single file folder or directory. By doing so, you keep all the files you need handy and avoid searching in several places every time you need them.

1.3. THE DIFFERENCE BETWEEN MEMORY AND STORAGE

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1.3. THE DIFFERENCE BETWEEN MEMORY AND STORAGE
People often confuse the terms memory and storage, especially when describing the amount they have of each. The term memory refers to the amount of RAM installed in the computer, whereas the term storage refers to the capacity of the computer’s hard disk. To clarify this common mix-up, it helps to compare your computer to an office that contains a desk and a file cabinet.

The file cabinet represents the computer's hard disk, which provides storage for all the files and information you need in your office. When you come in to work, you take out the files you need from storage and put them on your desk for easy access while you work on them. The desk is like memory in the computer: it holds the information and data you need to have handy while you're working.

Consider the desk-and-file-cabinet metaphor for a moment. Imagine what it would be like if every time you wanted to look at a document or folder you had to retrieve it from the file drawer. It would slow you down tremendously, not to mention drive you crazy. With adequate desk space – our metaphor for memory – you can lay out the documents in use and retrieve information from them immediately, often with just a glance.

Here’s another important difference between memory and storage: the information stored on a hard disk remains intact even when the computer is turned off. However, any data held in memory is lost when the computer is turned off. In our desk space metaphor, it’s as though any files left on the desk at closing time will be thrown away.

1.4. MEMORY AND PERFORMANCE

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1.4. MEMORY AND PERFORMANCE
It’s been proven that adding more memory to a computer system increases its performance. If there isn’t enough room in memory for all the information the CPU needs, the computer has to set up what’s known as a virtual memory file. In so doing, the CPU reserves space on the hard disk to simulate additional RAM. This process, referred to as “swapping”, slows the system down. In an average computer, it takes the CPU approximately 200ns (nanoseconds) to access RAM compared to 12,000,000ns to access the hard drive. To put this into perspective, this is equivalent to what’s normally a 3½ minute task taking 4½ months to complete!

Access time comparision between RAM and a hard drive.

MEMORY UPGRADE ON A PC: LIFE IS GOOD
If you've ever had more memory added to your PC, you probably noticed a performance improvement right away. With a memory upgrade, applications respond more quickly, Web pages load faster, and you can have more programs running simultaneously. In short, additional memory can make using your computer a lot more enjoyable.

MEMORY UPGRADE ON A SERVER: LIFE IS EVEN BETTER
These days, more and more people are using computers in a workgroup and sharing information over a network. The computers that help distribute information to people on a network are called servers. And their performance has a huge impact on the performance of the network: if a server is performing poorly, everyone on the network "feels the pain." So, while a memory upgrade on an individual PC makes a big difference for the person who uses it, a memory upgrade in a server has even more far-reaching effects and benefits everyone who accesses the server.

To better understand the benefits of increasing memory on a server, take a look at these results from an independent study done on Windows NT-based servers.

Application servers are utilized to host a wide range of applications, such as word processing and spreadsheet programs. By increasing base memory from 64MB to 256MB, Windows NT Server was able to support five times as many clients before transactions per second dropped.

Web servers are employed to serve up Web pages in response to HTTP requests from users. Doubling memory can cut response time by more than 50%.

Directory servers are vital to corporate productivity, handling most email and messaging tasks. In this environment, more memory increases the speed with which a server can access information from linked databases. Doubling memory increased performance from 248 to 3000%.

1.5. HOW MUCH MEMORY DO YOU NEED?

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1.5. HOW MUCH MEMORY DO YOU NEED?
Perhaps you already know what it's like to work on a computer that doesn't have quite enough memory. You can hear the hard drive operating more frequently and the "hour glass" or "wrist watch" cursor symbol appears on the screen for longer periods of time. Things can run more slowly at times, memory errors can occur more frequently, and sometimes you can't launch an application or a file without first closing or quitting another.

So, how do you determine if you have enough memory, or if you would benefit from more? And if you do need more, how much more? The fact is, the right amount of memory depends on the type of system you have, the type of work you're doing, and the software applications you're using. Because the right amount of memory is likely to be different for a desktop computer than for a server, we've divided this section into two parts - one for each type of system.

MEMORY REQUIREMENTS FOR A DESKTOP COMPUTER
If you're using a desktop computer, memory requirements depend on the computer's operating system and the application software you're using. Today's word processing and spreadsheet applications require as little as 32MB of memory to run. However, software and operating system developers continue to extend the capabilities of their products, which usually means greater memory requirements. Today, developers typically assume a minimum memory configuration of 64MB. Systems used for graphic arts, publishing, and multimedia call for at least 128MB of memory and it's common for such systems to require 256MB or more for best performance.

The chart on the next page provides basic guidelines to help you decide how much memory is optimal for your desktop computer. The chart is divided by operating system and by different kinds of work. Find the operating system you're using on your computer, then look for the descriptions of work that most closely match the kind of work you do.

DESKTOP MEMORY MAP
WINDOWS^® 2000 PROFESSIONAL
Windows 2000 Professional runs software applications faster. Notebook- ready and designed with the future in mind, Windows 2000 Professional allows users to take advantage of a full- range of features today. Windows 2000 Professional is future- ready and promises to run today's and tomorrow's applications better.
Baseline: 64MB - 128MB
Optimal: 128MB - 512MB
Administrative & Service Light- Word processing, email, data- entry 64MB - 96MB
Medium- Fax /communications, database administration, spreadsheets; >2 applications open at a time 64MB - 128MB
Heavy- Complex documents, accounting, business graphics, presentation software, network connectivity 96MB - 256MB
Executives & Analysts Light- Proposals, reports, spreadsheets, business graphics, databases, scheduling, presentations 64MB - 96MB
Medium- Complex presentations, sales/ market analysis, project management, Internet access 96MB - 128MB
Heavy- Statistical applications, large databases, research/ technical analysis, complex presentations, video conferencing 128MB - 512MB
Engineers&Designers Light- Page layout, 2 - 4 color line drawings, simple image manipulation, simple graphics 96MB - 128MB
Medium- 2D CAD, rendering, multimedia presentations, simple photo- editing, Web development 128MB - 512MB
Heavy- Animation, complex photo- editing, real- time video, 3D CAD, solid modeling, finite element analysis 256MB - 1GB

WINDOWS^® 98
Windows 98 requires 16 - 32MB to run basic applications. Tests show 45 - 65% performance improvements at 64MB and beyond.
Baseline: 32MB - 64MB
Optimal: 128MB - 256MB
Students Light- Word processing, basic financial management, email and other light Internet use 32MB - 64MB
Medium- Home office applications, games, Internet surfing, downloading images, spreadsheets, presentations 64MB - 128MB
Heavy- Multimedia use such as video, graphics, music, voice recognition, design, complex images 128MB - 384MB
Home Users Light- Word processing, basic financial management, email and other light Internet use 32MB - 48MB
Medium- Home office applications, games, Internet surfing, downloading images, spreadsheets, presentations 48MB - 64MB
Heavy- Multimedia use such as video, graphics, music, voice recognition, design, complex images 64MB - 128MB

LINUX^®
The Linux operating system is quickly gaining popularity as an alternative to Microsoft Windows. It includes true multitasking, virtual memory, shared libraries, demand loading, proper memory management, TCP/ IP networking, and other features consistent with Unix- type systems.
Baseline: 48MB - 112MB
Optimal: 112MB - 512MB
Administrative&Service Light- Word processing, email, data- entry 48MB - 80MB
Medium- Fax /communications, database administration, spreadsheets; >2 applications open at a time 48MB - 112MB
Heavy- Complex documents, accounting, business graphics, presentation software, network connectivity 80MB - 240MB
Executives&Analysts Light- Proposals, reports, spreadsheets, business graphics, databases, scheduling, presentations 48MB - 80MB
Medium- Complex presentations, sales/ market analysis, project management, Internet access 80MB - 112MB
Heavy- Statistical applications, large databases, research/ technical analysis, complex presentations, video conferencing 112MB - 512MB
Engineers&Designers Light- Page layout, 2 - 4 color line drawings, simple image manipulation, simple graphics 80MB - 112MB
Medium- 2D CAD, rendering, multimedia presentations, simple photo- editing, Web development 112MB - 512MB
Heavy- Animation, complex photo- editing, real- time video, 3D CAD, solid modeling, finite element analysis 240MB - 1GB

MACINTOSH^™ OS
The Macintosh operating system manages memory in substantially different ways than other systems. Still, System 9.0 users will find that 48MB is a bare minimum. When using PowerMac ^® applications with Internet connectivity, plan on a range between 64 and 128MB as a minimum.
Baseline: 48MB - 64MB
Optimal: 128MB - 512MB
Administrative&Service Light- Word processing, email, data- entry 48MB - 64MB
Medium- Fax /communications, database administration, spreadsheets; >2 applications open at a time 64MB - 96MB
Heavy- Complex documents, accounting, business graphics, presentation software, network connectivity 96MB - 128MB
Executives&Analysts Light- Proposals, reports, spreadsheets, business graphics, databases, scheduling, presentations 64MB - 256MB
Medium- Complex presentations, sales/ market analysis, project management, Internet access 128MB - 1GB
Heavy- Statistical applications, large databases, research/ technical analysis, complex presentations, video conferencing 96MB - 128MB
Engineers&Designers Light- Page layout, 2 - 4 color line drawings, simple image manipulation, simple graphics 128MB - 512MB
Medium- 2D CAD, rendering, multimedia presentations, simple photo- editing, Web development 256MB - 1GB
Heavy- Animation, complex photo- editing, real- time video, 3D CAD, solid modeling, finite element analysis 512MB - 2GB

* Please Note: These figures reflect work done in a typical desktop environment. Higher-end workstation tasks may require up to 4GB. Naturally, a chart such as this evolves as memory needs and trends change. Over time, developers of software and operating systems will continue to add features and functionality to their products. This will continue to drive the demand for more memory. More complex character sets, like Kanji, may require more memory than the standard Roman based (English) character sets.

SERVER MEMORY REQUIREMENTS
How can you tell when a server requires more memory? Quite often, the users of the network are good indicators. If network-related activity such as email, shared appli-cations, or printing slows down, they'll probably let their Network Administrator know. Here are a few proactive strategies that can be used to gauge whether or not a server has sufficient memory:

Monitor server disk activity. If disk swapping is detected, it is usually a result of inadequate memory.

Most servers have a utility that monitors CPU, memory, and disk utilization. Review this at peak usage times to measure the highest spikes in demand.
Once it's determined that a server does need more memory, there are many factors to consider when deciding on how much is enough:

What functions does the server perform (application, communication, remote access, email, Web, file, multimedia, print, database)?

Some servers hold a large amount of information in memory at once, while oth-ers process information sequentially. For example, a typical large database server does a lot of data processing; with more memory, such a server would likely run much faster because more of the records it needs for searches and queries could be held in memory - that is, "at the ready." On the other hand, compared to a database server, a typical file server can perform efficiently with less memory because its primary job is simply to transfer information rather than to process it.
What operating system does the server use?

Each server operating system manages memory differently. For example, anetwork operating system (NOS) such as the Novell operating system handles information much differently than an application-oriented system such as Windows NT. Windows NT's richer interface requires more memory, while the traditional Novell functions of file and print serving require less memory.
How many users access the server at one time?

Most servers are designed and configured to support a certain number of users at one time. Recent tests show that this number is directly proportional to the amount of memory in the server. As soon as the number of users exceeds maximum capacity, the server resorts to using hard disk space as virtual memory, and performance drops sharply. In recent studies with Windows NT, additional memory allowed an application server to increase by several times the number of users supported while maintaining the same level of performance.
What kind and how many processors are installed on the server?

Memory and processors affect server performance differently, but they work hand in hand. Adding memory allows more information to be handled at one time, while adding processors allows the information to be processed faster. So, if you add processing power to a system, additional memory will enable the processors to perform at their full potential.
How critical is the server's response time?

In some servers, such as Web or e-commerce servers, response time directly affects the customer experience and hence revenue. In these cases, some IT Managers choose to install more memory than they think they would ever need in order to accommodate surprise surges in use. Because server configurations involve so many variables, it's difficult to make precise recommendations with regard to memory. The following chart shows two server upgrade scenarios.
SERVER MEMORY MAP
WINDOWS^® 2000 SERVER
Designed to help businesses of all sizes run better, Windows 2000 Server offers a manageable, reliable and internet- ready solution for today's growing enterprises. For optimal performance, consider adding more memory to take advantage of Windows 2000 Server's robust feature set. Windows 2000 Server is internet- ready and promises to run today's and tomorrow's applications better.
Baseline: 128MB
Optimal: 256MB - 1GB
Application Server Houses one or more applications to be accessed over a wide user base 256MB - 4GB
Directory Server Central Management of network resources 128MB - 1GB
Print Server Distributes print jobs to appropriate printers 128MB - 512MB
Communication Server Manages a variety of communications such as PBX, Voicemail, Email, and VPN 512MB - 2GB
Web Server Internet and intranet solutions 512MB - 2GB
Database Server Manages simple to complex databases of varying sizes 256MB - 4GB

LINUX^®
Linux is a reliable, cost- effective alternative to traditional UNIX servers. Depending on the distribution, the Linux server platform features a variety of utilities, applications, and services.
Baseline: 64MB - 128MB
Optimal: 256MB - 1GB
Application Server Houses one or more applications to be accessed over a wide user base 64MB - 4GB
Directory Server Central Management of network resources 128MB - 1GB
Print Server Distributes print jobs to appropriate printers 128MB - 512MB
Communication Server Manages a variety of communications such as PBX, Voicemail, Email, and VPN 512MB - 2GB
Web Server Internet and intranet solutions 512MB - 2GB
Database Server Manages simple to complex databases of varying sizes 256MB - 4GB

* Please Note: These figures reflect work done in a typical server environment. Higher- end workstation tasks may require up to 4GB. Naturally, a chart such as this evolves as memory needs and trends change. Over time, developers of software and operating systems will continue to add features and functionality to their products. This will continue to drive the demand for more memory. More complex character sets, like Kanji, may require more memory than the standard Roman based (English) character sets.

10. Choice of Table Size

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Choice of Table Size
It is desirable that the stored filter impulse response be sampled sufficiently densely so that interpolating linearly between samples does not introduce error greater than the quantization error. We will show that this condition is satisfied whenever the filter table contains at least entries per zero-crossing, where is the number of bits allocated to each table entry.

10. Difference Equation

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Difference Equation
Definition. The difference equation for a general linear time-invariant (LTI)digital filter is given by
(42)
(43)

10. Getting the Most from your Batteries

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10. Getting the Most from your Batteries
A common difficulty with portable equipment is the gradual decline in battery performance after the first year of service. Although fully charged, the battery eventually regresses to a point where the available energy is less than half of its original capacity, resulting in unexpected downtime.
Downtime almost always occurs at critical moments. This is especially true in the public safety sector where portable equipment runs as part of a fleet operation and the battery is charged in a pool setting, often with minimal care and attention. Under normal conditions, the battery will hold enough power to last the day. During heavy activities and longer than expected duties, a marginal battery cannot provide the extra power needed and the equipment fails.

10. Getting the Most from your Batteries 2

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10.2 How to Restore and Prolong Nickel-based Batteries

The effects of crystalline formation are most pronounced if a nickel-based battery is left in the charger for days, or if repeatedly recharged without a periodic full discharge. Since most applications do not use up all energy before recharge, a periodic discharge to 1V/cell (known as exercise) is essential to prevent the buildup of crystalline formation on the cell plates. This maintenance is most critical for the NiCd battery.

10. Getting the Most from your Batteries 3

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After service, the restored batteries were returned to full use. When examined after six months of field use, no noticeable degradation in the restored performance was visible. The regained capacity was permanent with no evidence of falling back to the previous state. Obviously, the batteries would need to be serviced on a regular basis to maintain the performance.

Applying the recondition cycle on a new battery (top line on chart) resulted in a slight capacity increase. This capacity gain is not fully understood, other than to assume that the battery improved by additional formatting. Another explanation is the presence of early memory. Since new batteries are stored with some charge, the self-discharge that occurs during storage contributes to a certain amount of crystalline formation. Exercising and reconditioning reverse this effect. This is why the manufacturers recommend storing rechargeable batteries at about 40 percent charge.

10. Getting the Most from your Batteries 4

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10.3 The Effect of Zapping

To maximize battery performance, remote control (RC) racing enthusiasts have experimented with all imaginable methods available. One technique that seems to work is zapping the cells with a very high pulse current. Zapping is said to increase the cell voltage slightly, generating more power.

Typically, the racecar motor draws 30A, delivered by a 7.2V battery. This calculates to over 200W of power. The battery must endure a race lasting about four minutes.

10. Getting the Most from your Batteries 5

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10.4 How to Restore and Prolong Sealed Lead Acid Batteries

The sealed version of the lead acid battery is designed with a low over-voltage potential to prevent water depletion. Consequently, the SLA and VRLA systems never get fully charged and some sulfation will develop over time.

Finding the ideal charge voltage limit for the sealed lead acid system is critical. Any voltage level is a compromise. A high voltage limit produces good battery performance, but shortens the service life due to grid corrosion on the positive plate. The corrosion is permanent and cannot be reversed. A low voltage preserves the electrolyte and allows charging under a wide temperature range, but is subject to sulfation on the negative plate. (In keeping with portability, this book focuses on portable SLA batteries. Due to similarities between the SLA and VRLA systems, references to the VRLA are made where applicable).

10. Getting the Most from your Batteries 6

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10.5 How to Prolong Lithium-based Batteries

Today’s battery research is heavily focused on lithium chemistries, so much so that one could assume that all future batteries will be lithium systems. Lithium-based batteries offer many advantages over nickel and lead-based systems. Although maintenance free, no external service is known that can restore the battery’s performance once degraded.

In many respects, Li-ion provides a superior service to other chemistries, but its performance is limited to a defined lifespan. The Li-ion battery has a time clock that starts ticking as soon as the battery leaves the factory. The electrolyte slowly ‘eats up’ the positive plate and the electrolyte decays. This chemical change causes the internal resistance to increase. In time, the cell resistance raises to a point where the battery can no longer deliver the energy, although it may still be retained in the battery. Equipment requiring high current bursts is affected most by the increase of internal resistance.

10. Getting the Most from your Batteries 7

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10.6 Battery Recovery Rate

The battery recovery rate by applying controlled discharge/charge cycles varies with chemistry type, cycle count, maintenance practices and age of the battery. The best results are achieved with NiCd. Typically 50 to 70 percent of discarded NiCd batteries can be restored when using the exercise and recondition methods of a Cadex battery analyzer or equivalent device.

Not all batteries respond equally well to exercise and recondition services. An older battery may show low and inconsistent capacity readings with each cycle. Another will get worse when additional cycles are applied. An analogy can be made to a very old man for whom exercise is harmful. Such conditions indicate instabilities caused by aging, suggesting that this pack should be replaced. In fact, some users of the Cadex analyzers use the recondition cycle as the acid test. If the battery gets worse, there is strong evidence that this battery would not perform well in the field. Applying the acid test exposes the weak packs, which can no longer hide behind their stronger peers.

10. THE GLOSSARY

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10. THE GLOSSARY
#A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Accelerated Graphics Port: (AGP) – An Intel-developed interface that enables high-speed graphics. Graphics data move between the PC’s graphics controller and computer memory directly, instead of being cached in video memory.
Access Time: The average time (in nanoseconds) for RAM to complete one access. Access time is composed of address setup time and latency (the time it takes to initiate a request for data and prepare access).
ANSI: (American National Standards Institute) – The U.S. organization responsible for setting information technology standards.
ASCII: (American Standard Code for Information Interchange) – A method of encoding text as binary values. The ASCII coding system contains 256 combinations of 7-bit or 8-bit binary numbers to represent every possible keystroke.
Backside Bus: (BSB) – The data path that runs between the CPU and L2 cache. The amount of data moved on electronic lines, such as a bus, per second.
Bandwidth: Bandwidth is usually measured in bits per second, bytes per second, or cycles per second (Hertz).
Bank: See memory bank.
Bank Schema: A method of diagramming memory configurations. The bank schema consists of rows and/or columns that represent memory sockets on a computer board. Rows indicate independent sockets; columns represent banks.
Base Rambus: The first generation of Rambus technology, first shipped in 1995.
BGA: (Ball Grid Array) – A chip package having solder balls on the underside for mounting. BGA allows for a reduction in die package size, better heat dissipation, and greater module densities.
Binary: A numbering system that uses combinations of 0 and 1 to represent data. Also known as Base 2.
BIOS: (Basic Input-Output System) – Startup routines that prepare the computer for operation.
Bit: The smallest unit of information a computer processes. A bit is 1 or 0.
Buffer: A holding area for data shared by devices that operate at different speeds or have different priorities. A buffer allows a device to operate without the delays that other devices impose.
Buffered Memory: A memory module that contains buffers. Buffers re-drive the signals through the memory chips and allow the module to include more memory chips. Buffered and unbuffered memory cannot be mixed. The design of the computer memory controller dictates whether memory must be buffered or unbuffered.
Burst EDO RAM: (BEDO) – EDO memory that can process four memory addresses in one burst. Bus speeds range from 50MHz to 66MHz (compared to 33MHz for EDO and 25MHz for Fast Page Mode).
Burst Mode: High-speed transmission of a block of data (a series of consecutive addresses) when the processor requests a single address.
Bus: A data path in a computer, consisting of various parallel wires to which the CPU, memory, and all input/output devices are connected.
Bus Cycle: A single transaction between main memory and the CPU.
Byte: Eight bits of information. The byte is the fundamental unit of computer processing; almost all specifications and measures of computer performance are in bytes or multiples thereof. See kilobytes and megabytes.
Cache Memory: A small amount (normally less than 1MB) of high-speed memory residing on or close to the CPU. Cache memory supplies the processor with the most frequently requested data and instructions. Level 1 cache (primary cache) is the cache closest to the processor. Level 2 cache (secondary cache) is the cache second closest to the processor and is usually on the motherboard.
CAS: (Column Address Strobe) – A memory chip signal that latches the column address of a particular location in a row-column matrix.
CAS Latency: The ratio between column access time and clock cycle time. CAS Latency 2 (CL2) offers a slight performance increase over CAS Latency 3 (CL3).
ccNUMA: (Cache-Coherent, Non-uniform Memory Access) – A flexible architecture that uses modular, low-cost components and offers multidimensional scaling potential to high-end servers.
Chipset: Microchips that support the CPU. The chipset usually contains several controllers that govern how information travels between the processor and other components.
Chip-Scale Package: (CSP) – Thin chip packaging whereby electrical connections are typically through a ball grid array. Chip-scale packaging is used in RDRAM and flash memory.
CompactFlash: A small, lightweight form factor for removable storage cards. CompactFlash cards are durable, operate at low voltages, and retain data when power is off. Uses include digital cameras, cell phones, printers, handheld computers, pagers, and audio recorders.
Composite: An Apple Computer, Inc. term for a memory module that used an older technology and contained more but lower-density chips.
Concurrent Rambus: The second generation of Rambus technology. Concurrent Rambus has been used in graphics-based computers, digital TVs, and video game applications (such as Nintendo 64 since 1997).
Continuity RIMM: (C-RIMM) – A Direct Rambus memory module that does not contain memory chips. C-RIMM provides a continuous channel for the signal. In a Direct Rambus system, open connectors must be populated with C-RIMMs.
CPU: (Central Processing Unit) – The computer chip that has primary responsibility for interpreting commands and running programs. The CPU is also known as the processor or microprocessor.
Credit Card Memory: A type of memory typically in laptop and notebook computers. Credit card memory is the size of a credit card.
DDR SDRAM: (Double Data Rate Synchronous Dynamic Random-Access Memory) – The latest generation of SDRAM technology. Data is read on both the rising and the falling edge of the computer clock, thereby delivering twice the bandwidth of standard SDRAM. With DDR SDRAM, memory speed doubles without increasing the clock frequency.
DIMM: (Dual In-line Memory Module) – A printed circuit board with gold contacts and memory devices. A DIMM is similar to a SIMM, but with this primary difference: unlike the metal leads on either side of a SIMM, which are “tied together” electrically, the leads on either side of a DIMM are electrically independent.
Direct Rambus: Rambus technology’s third generation, which offers a completely new DRAM architecture for high-performance PCs. Data transfers at speeds up to 800MHz over a narrow 16-bit channel, compared to current SDRAM, which operates at 100MHz on a wide 64-bit bus.
DIP: (Dual In-line Package) – A DRAM component packaging. DIPs can be installed in sockets or permanently soldered into holes on the printed circuit board. The DIP package was extremely popular when memory was installed directly on the motherboard.
DRAM: (Dynamic Random-Access Memory) – The most common form of RAM. DRAM can hold data for only a short time. To retain data, DRAM must be refreshed periodically. If the cell is not refreshed, the data disappear.
Dual-Banked: A memory module having two banks.
Dual Independent Bus: (DIB) – An Intel-developed bus architecture that offers greater bandwidth by having two separate buses (frontside and backside) access the processor. Pentium II computers have DIBs.
ECC: (Error Correction Code) – A method of checking the integrity of data in DRAM. ECC provides more elaborate error detection than parity; ECC can detect multiple-bit errors and can locate and correct single-bit errors.
EDO: (Extended Data-Out) – A DRAM technology that shortens the read cycle between memory and CPU. On computers that support it, EDO memory allows a CPU to access memory 10 to 20 percent faster than comparable fast-page mode memory.
EDRAM: (Enhanced DRAM) – Enhanced Memory Systems, Inc. DRAM that contains a small amount of SRAM.
EEPROM: (Electrically Erasable Programmable Read-Only Memory) – A memory chip that retains data content after power has been removed. EEPROM can be erased and reprogrammed within the computer or externally.
EISA: (Extended ISA) – A bus architecture that extended the 16-bit ISA bus to 32 bits. EISA operates at 8MHz and has a peak data transfer rate of 33MB per second. EISA was introduced in 1988 as an open alternative to IBM’s proprietary Micro Channel bus.
EOS: (ECC on SIMM) – An IBM data-integrity-checking technology that features ECC data-integrity-checking on a SIMM.
EPROM: (Erasable Programmable Read-Only Memory) – A programmable and reusable chip that retains content until erasure under ultraviolet light. Special equipment erases and reprograms EPROMs.
ESDRAM: (Enhanced Synchronous DRAM) – A type of SDRAM developed by Enhanced Memory Systems, Inc. ESDRAM replaces expensive SRAM in embedded systems and offers comparable speed with less power consumption and lower cost.
Even Parity: A type of data integrity checking whereby the parity bit checks for an even number of 1s.
Fast-Cycle RAM: (FCRAM) – FCRAM is a memory technology currently being developed by Toshiba and Fujitsu. FCRAM is not intended for PC main memory but will be used in specialty applications such as high-end servers, printers, and telecommunications switching systems.
Fast-Page Mode: An early form of DRAM, fast-page mode’s advantage over previous page mode memory technologies was faster access to data in the same row.
Flash Memory: A solid-state, nonvolatile, rewritable memory that functions like a combination of RAM and hard disk. Flash memory is durable, operates at low voltages, and retains data when power is off. Flash memory cards are used in digital cameras, cell phones, printers, handheld computers, pagers, and audio recorders.
Form Factor: The size, configuration, and other specifications used to describe hardware. Examples of memory form factors are: SIMM, DIMM, RIMM, 30-pin, 72-pin, and 168-pin.
Frontside Bus: (FSB) – The data path that runs between the CPU and main memory (RAM).
Gigabit: Approximately 1 billion bits, or exactly 1 bit x 1,0243 (1,073,741,824) bits.
Gigabyte: Approximately 1 billion bytes, or exactly 1 byte x 1,0243 (1,073,741,824) bytes.
Heat Spreader: A sheath, usually aluminum, that covers an electronic device and dissipates heat.
Heat Sink: A component, typically zinc alloy, that dissipates heat. CPUs require heat sinks.
IC: (Integrated Circuit) – An electronic circuit on a semiconductor chip. The circuit includes components and connectors. A semiconductor chip is usually molded in a plastic or ceramic case and has external connector pins.
Interleaving: Techniques for increasing memory speed. For example, with separate memory banks for odd and even addresses, the next byte of memory can be accessed while the current byte refreshes.
JEDEC: (Joint Electron Device Engineering Council) – An Electronic Industries Alliance (EIA) body that sets semiconductor engineering standards.
Kilobit: Approximately one thousand bits, or exactly 1 bit x 210 (1,024) bits.
Kilobyte: Approximately one thousand bytes, or exactly 1 byte x 210 (1,024) bytes.
Level 1 Cache: (L1) – Also known as primary cache, L1 Cache is a small amount of high-speed memory that resides on or very close to the processor. L1 Cache supplies the processor with the most frequently requested data and instructions.
Level 2 Cache: (L2) – Also known as secondary cache, L2 Cache is a small amount of high-speed memory close to the CPU and usually on the motherboard. L2 Cache supplies the processor with the most frequently requested data and instructions. Depending on the motherboard, Level 2 cache may be upgraded.
Logic Board: See Motherboard.
Megabit: Approximately one million bits, or exactly 1 bit x 1,0242 (1,048,576) bits.
Megabyte: Approximately one million bytes, or exactly 1 byte x 1,0242 (1,048,576) bytes.
Memory: A computer’s random-access memory. Memory temporarily holds data and instructions for the CPU. See RAM.
Memory Bank: A logical unit of memory in a computer, the size of which the CPU determines. For example, a 32-bit CPU requires memory banks that provide 32 bits of information at a time. A bank can consist of one or more memory modules.
Memory Bus: The bus that runs from the CPU to the memory expansion slots.
Memory Controller Hub: (MCH) – The interface between the processor, Accelerated Graphics Port, and RDRAM on motherboards that use Intel’s 820 or 840 chipsets.
Memory Translator Hub: (MTH) – The interface that allows SDRAM memory to be supported on a Direct Rambus Channel for motherboards using Intel’s 820 chipset.
Micro BGA: (µBGA) – Tessera, Inc. BGA chip packaging technique allows for a reduction in die package size, improved heat dissipation, and greater module densities.
Motherboard: Also known as the logic board, main board, or computer board, the motherboard is the computer’s main board and in most cases holds all CPU, memory, and I/O functions or has expansion slots for them.
Nanosecond: (ns) – One billionth of a second. Memory data access times are in nanoseconds. For example, memory access times for typical 30- and 72-pin SIMM modules range from 60 to 100 nanoseconds.
Nibble: Half of an 8-bit byte, or 4 bits.
Non-Composite: An Apple Computer, Inc. term for a memory module that used a new technology and contained fewer but higher-density chips. Non-composite modules were more reliable and more expensive than composite modules.
Odd Parity: Data integrity checking in which the parity bit checks for an odd number of 1s.
Parity: Data integrity checking that adds a single bit to each byte of data. The parity bit is used to detect errors in the other 8 bits.
PCB: (Printed Circuit Board) – Generally flat, multi-layer boards made of fiberglass with electrical traces. The surface and sublayers use copper traces to provide electrical connections for chips and other components. Examples of PCBs include: motherboards, SIMMs, and credit card memory.
PC Card: (PCMCIA: Personal Computer Memory Card International Association) – A standard that allows interchangeability of various computing components on the same connector. The PCMCIA standard supports input-output devices, including memory, fax/modem, SCSI, and networking products.
PCI: (Peripheral Component Interconnect) – A peripheral bus that can send 32 or 64 bits of data simultaneously. PCI offers plug-and-play capability.
Pipeline Burst Cache: Cache that reduces wait states and accelerates memory access by using pipelining and bursting functions.
Pipelining: A technique in which memory loads the requested memory contents into a small cache composed of SRAM, then immediately begins fetching the next memory contents. This creates a two-stage pipeline, where data is read from or written to SRAM in one stage, and data is read from or written to memory in the other stage.
Proprietary Memory: Memory custom designed for a specific computer.
RAM: (Random-Access Memory) – A memory cell configuration that holds data for processing by a central processing unit (CPU). Random means the CPU can retrieve data from any address within RAM. See also Memory.
Rambus: (1) Rambus, Inc. develops and licenses high-performance memory logic and circuit design technology and provides licensees with product design, layout, and testing information. (2) Direct Rambus is a high-speed memory technology that uses a narrow 16-bit bus
Rambus Channel: (Rambus channel) to transmit data at speeds up to 800MHz. See Rambus Channel. The data path of Rambus systems. Because of the narrow data width (two bytes), Rambus modules transfer data at up to 800MHz.
RAS: A memory chip signal that latches the row address of a particular location in a row-column matrix.
Refresh: Refreshing maintains data stored in DRAM. The process of refreshing electrical cells on a DRAM component is similar to recharging batteries. Different DRAM components require different refresh methods.
Refresh Rate: The number of DRAM component rows that must be refreshed. Three common refresh rates are 2K, 4K and 8K.
Registered Memory: SDRAM memory that contains registers directly on the module. The registers re-drive the signals through the memory chips and allow the module to be built with more memory chips. Registered and unbuffered memory cannot be mixed. The design of the computer memory controller dictates which type of memory the computer requires.
RIMM^TM: The trademarked name for a Direct Rambus memory module. A RIMM™ conforms to the DIMM form factor and transfers data 16 bits at a time.
RIMM Connector: A Direct Rambus memory socket.
SDRAM: (Synchronous DRAM) – A DRAM technology that uses a clock to synchronize signal input and output on a memory chip. The clock is coordinated with the CPU clock so the timing of the memory chips and the timing of the CPU are in synch. Synchronous DRAM saves time in executing commands and transmitting data, thereby increasing the overall performance of the computer. SDRAM allows the CPU to access memory approximately 25 percent faster than EDO memory.
Self-Refresh: A memory technology that enables DRAM to refresh on its own and independent of the CPU or external refresh circuitry. Self-Refresh technology is built into the DRAM chip itself and reduces power consumption dramatically. Notebook and laptop computers use this technology.
Serial Presence Detect: An EEPROM chip that contains information about size and speed, as well as other specifications and manufacturer information of a memory module.
SGRAM: (Synchronous Graphics Random-Access Memory) – Video memory that includes graphicsspecific read/write features. SGRAM allows data to be retrieved and modified in blocks instead of individually. Blocking reduces the number of reads and writes the memory must perform and increases the performance of the graphics controller.
SIMM: (Single In-line Memory Module) – A printed circuit board having memory devices and gold or tin/lead contacts. A SIMM plugs into a computer memory expansion socket. SIMMs offer two main advantages: ease of installation and minimal consumption of board surface. A vertically mounted SIMM requires only a fraction of the space required by a horizontally mounted DRAM. A SIMM may have as few as 30 or as many as 200 pins. On a SIMM, the metal leads on either side of the board are electrically tied together.
SIMM Socket: A motherboard component that holds a single SIMM.
Single-Banked: A module that has only one bank or row.
SLDRAM: (Synclink) – Although obsolete today, SLDRAM was a main memory technology developed by a consortium of twelve DRAM manufacturers as an alternative to Direct Rambus technology.
SMART CARD: An electronic device, similar in size to a credit card, that can store data and programs while enhancing security. Applications include identification, mass transit, and banking.
SO DIMM: (Small-Outline Dual In-line Memory Module) – An enhanced version of a standard DIMM. A 72-pin small-outline DIMM is about half the length of a 72-pin SIMM. The trademarked name for a Direct Rambus memory module in notebook computers.
SO-RIMM^TM: SO-RIMM™s provide memory bandwidth comparable to desktop memory configurations.
SOJ: (Small-Outline J-lead) – A common form of surface-mounted DRAM packaging. An SOJ is a rectangular package with J-shaped leads on the two long sides.
Static RAM: (SRAM) – A memory chip that requires power to retain content. SRAM is faster than DRAM but more expensive and bulky. A typical use for SRAM is cache memory.
Storage: A data-holding device, such as a hard disk or CD-ROM.
Swapping: Using part of the hard drive as memory when RAM is full. See Virtual Memory.
System Board: See Motherboard.
Transmission Line Technology: A technology that supports the backside bus in Direct Rambus systems.Information is quickly pipelined in simultaneous packets. The memory controller reassembles the packets for frontside bus transfer and communication to the processor.
TSOP: (Thin Small-Outline Package) – A DRAM package that uses gull-wing leads on both sides. TSOP DRAM mounts directly on the surface of the printed circuit board. The TSOP package is one-third the thickness of an SOJ. TSOP components commonly occur in small-outline DIMMs and credit card memory.
Unbuffered Memory: Memory that does not contain buffers or registers located on the module. Instead, these devices are located on the motherboard.
VESA Local Bus: (VL-Bus) – A 32-bit local bus that runs between the CPU and peripheral devices at speeds up to 40MHz.
Virtual Channel Memory: (VCM) – VCM is a memory architecture developed by NEC. VCM allows different blocks of memory–each with its own buffer–to interface separately with the controller. This way, system tasks can be assigned their own virtual channels.
Virtual Memory: Information related to one function does not share buffer space with other tasks running simultaneously, thereby making overall operations much more efficient. Simulated memory. When RAM is full, the computer swaps data to the hard disk and back as needed. See Swapping.
VRAM: (Video Random-Access Memory) – Dual-ported (two separate data ports) memory typically on a video or graphics card. One port is dedicated to the CRT and refreshes and updates the image. The second port is for the CPU or graphics controller and changes the image data in memory.
Wait State: An inactive period for the processor. Wait states result from the different clock speeds of the processor and memory, the latter being typically slower.
Window Random Access Memory: (WRAM) – Samsung Electronics’ dual-ported (two separate data ports) memory typically on a video or graphics card. WRAM has a 25% higher bandwidth than VRAM but costs less.

11. Choice of Interpolation Resolution

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Choice of Interpolation Resolution
We now consider the error due to finite precision in the linear interpolation between stored filter coefficients. We will find that the number of bits in the interpolation factor should be about half the filter coefficient word-length .

11. Convolution Representation

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Convolution Representation
If is the output of an LTI filter with input and impulseresponse , then is the convolution of with ,

11. Maintaining Fleet Batteries

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11. Maintaining Fleet Batteries

Unlike individual battery users, who come to know their batteries like a good friend, fleet users must share the batteries from a pool of unknown packs. While an individual user can detect even a slight reduction in runtime, fleet operators have no way of knowing the behavior or condition of the battery when pulling it from the charger. They are at the mercy of the battery. It’s almost like playing roulette.

11. Maintaining Fleet Batteries 2

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11.1 The ‘Green Light’ Lies

When charging a battery, the ready light will eventually illuminate, indicating that the battery is fully charged. The user assumes that the battery has reached its full potential and the battery is taken in confidence.

In no way does the ‘green light’ guarantee sufficient battery capacity or assure good state-of-health (SoH). Similar to a toaster that pops up the bread when brown (or black), the charger fills the battery with energy and ‘pops’ it to ready when full (or warm).

11. Maintaining Fleet Batteries 3

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11.2 Battery Maintenance, a Function of Quality Control

The reliability of portable equipment relies almost entirely on the performance of the battery. A dependable battery fleet can only be assured if batteries are maintained on a periodic basis.

Battery maintenance also needs proper documentation. One simple method is attaching a color dot, each color indicating the month of service. A different color dot is applied when the battery is re-serviced the following month. A numbering system indicating the month of service also works well.

12. Battery Maintenance Equipment

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12. Battery Maintenance Equipment
With the increasing volume of batteries in circulation, battery manufacturing is outpacing the supply of suitable equipment to test these packs. This void is especially apparent in the mobile phone market where large quantities of batteries are being replaced under warranty without checking or attempting to restore them. The dealers are simply not equipped to handle the influx of returned batteries, neither is the staff trained to perform this task on a customer service level. Testing and conditioning these batteries is a complex procedure that lies outside the capabilities of most customer service clerks.

12. Battery Maintenance Equipment 2

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12.2 Battery Analyzers

There are two types of battery analyzers: the fixed current units and the programmable devices. While fixed current units are less expensive and generally simpler to operate, programmable analyzers are more accurate and faster. Programmable units can better adapt to different battery needs and are more effective in restoring weak batteries. One of the main advantages of the programmable battery analyzer is the ability to test the batteries against preset parameters.

12. Battery Maintenance Equipment 3

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Battery-specific adapters are available for all major batteries; user-programmable cables with alligator clips accommodate batteries for which no adapter is on hand. Batteries with shorted, mismatched or soft cells are identified in minutes and their deficiencies are displayed on the LCD panel.

User-selectable programs address different battery needs. The Cadex 7000 Series features ‘Prime’ to prepare a new battery for field use and ‘Auto’ to test and recondition weak batteries from the field. ‘Custom’ allows the setting of unique cycle sequences composed of charge, discharge, recondition, trickle charge or any combination, including rest periods and repeats.

12. Battery Maintenance Equipment 4

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12.3 Battery Analyzers for Maintenance-Free Batteries

In the past, the purpose of battery analyzers was to restore NiCd batteries affected by ‘memory’. With today’s nickel-free batteries, memory is no longer a problem and the modern battery analyzer assumes duties other than conditioning weak batteries. In an environment with nickel-free batteries, the purpose of an analyzer is shifting to performance verification, quality control, quick testing and quick priming.

12. Battery Maintenance Equipment 5

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12.5 Battery Maintenance Software

Organizations servicing portable equipment need simplified battery testing. The difficulty of testing batteries is brought on by the proliferation of batteries, both in volume and diversity of models. With most standalone battery test equipment, servicing batteries with conventional methods is complex and time consuming. This task will only get more difficult as new battery models are added, almost weekly. New chemistries are being introduced which have different service requirements.

12. Conclusions

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Conclusions
A digital resampling method has been described which is convenient forbandlimited interpolation at arbitrary times and for smoothly varyingsampling rates, and which is attractive for hardware implementation. We have presented the case which assumes uniform sampling of the input signal; however, extensions to variable sampling rates and isolated-point evaluation are straightforward.

12. Frequency Response

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Frequency Response
Beginning with Eq. (2.2.1), we have

where is the -transform of the filter input, is the -transform of the output signal, and is the filter transfer function.
Definition. The frequency response of a linear time-invariant digital filter is defined to be the transfer function, , evaluated on the unit circle, that is, .

13. Exact Sinc-Interpolation of Sampled Periodic Signals

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Appendix A: Exact Sinc-Interpolation of Sampled Periodic Signals
It turns out all periodic sampled signals can be sinc-interpolatedexactly using the following formula [Schanze 1995]:

13. Making Battery Quick-Test Feasible

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13. Making Battery Quick-Test Feasible
When Sanyo, one of the largest battery manufacturers in the world, was asked, “Is it feasible to quick test batteries?” the engineer replied decisively, “No”. He based his conclusion on the difficulty of using a universal test formula that applies to all battery applications, — from wireless communications to mobile computing, and from power tools to forklifts and electric vehicles.
Several universities, research organizations and private companies, including Cadex, are striving to find a workable solution to battery quick testing. Many methods have been tried, and an equal number have failed because they were inaccurate, inconsistent and impractical.

13. Making Battery Quick-Test Feasible 2

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13.2 Three-Point Quick Test

The three-point quick test uses internal battery impedance as a basis and adds the battery voltage under charge and discharge to the equation. The readings are evaluated and compared with reference settings stored in the tester. Let’s explore each of these fundamentals closer to see what it entails:

Internal resistance — To measure the impedance, a battery must be at least 50 percent charged. An empty or nearly empty battery exhibits a high internal resistance. As the battery reaches 50 percent SoH, the resistance drops, then increases again towards full discharge or full charge. Figure 13-1 shows the typical internal resistance curve of a NiMH as a function of charge. Note the decrease of impedance after the battery has rested for a while. To obtain accurate results, allow the battery to rest after discharge and charge.

13. Making Battery Quick-Test Feasible 3

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13.3 The Evolving Battery

The Li-ion battery has not yet matured. Chemical compositions change as often as once every six months. According to Moli Energy, a large manufacturer of Li-ion batteries, the chemical composition of Li-based batteries changes every six months. New chemicals are discovered that provide better load characteristics, higher capacities and longer storage life. Although beneficial to consumers, these improvements wreak havoc with battery testing equipment that base quick test algorithms on fixed parameters. Why do these changes in battery composition affect the results of a quick tester?

13. Making Battery Quick-Test Feasible 4

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13.5 How does the Cadex Quicktest work?

The first stage of the Cadex Quicktest™analysis uses a waveform to gather battery information under certain stresses, establishing probability levels for the given battery. Since there are many battery types with several interacting variables, a set of rules is applied to further evaluate the data. The results are averaged and an estimated battery capacity is predicted. The initial inference to categorize the batteries is computed from a set of specialized shapes called membership functions. These membership functions are unique to every battery model and are developed using a specialized trend-learning algorithm.

13. Making Battery Quick-Test Feasible 5

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13.7 Electrochemical Impedance Spectroscopy

Electrochemical Impedance Spectroscopy (EIS) has been used for a number of years to test the SoH and SoC of industrial batteries. EIS is well suited for observing reactions in the kinetics of electrodes and batteries. Changes in impedance readings hint at minute intrusion of corrosion, which can be evaluated with the EIS methods. Impedance studies using the EIS technology have been carried out on lead acid, NiCd, NiMH, Li-ion and other chemistries. EIS test methods are also used to examine the cells on larger stationary batteries.

13. Phase Delay and Group Delay

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Phase Delay and Group Delay
The phase response of a filter gives the radian phase shift experienced by each sinusoidal component of the input signal. Sometimes it is more meaningful to consider phase delay[Papoulis 1977].

14. Appendix B: Relation between Sinc and Lagrange Interpolation

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Appendix B: Relation between Sinc and Lagrange Interpolation
Lagrange interpolation is a well known, classical technique for interpolation [Hildebrand 1974]. Given a set of known samples, , the problem is to find the unique order polynomial which interpolates the samples. The solution can be expressed as a linear combination of elementary th order polynomials:

14. Non-Correctable Battery Problems

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14. Non-Correctable Battery Problems
Non-correctable battery problems are those that cannot be improved through external means such as giving the battery a full charge or by applying repeated charge/discharge cycles. Deficiencies that denote the non-correctable status are high internal resistance, elevated self-discharge, electrical short of one or several cells, lack of electrolyte, oxidation, corrosion and general chemical breakdown. These degenerative effects are not only caused by normal usage and aging, but they include less than ideal field conditions and an element of neglect. The user may have poor charging equipment, may operate and store the battery in adverse temperatures and, in the case of nickel-based batteries, may not maintain the battery properly.

14. Non-Correctable Battery Problems 2

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14.2 Low Capacity Cells

Even with modern manufacturing techniques, the capacity of a cell cannot be accurately predicted. As part of the manufacturing process, each cell is measured and segregated into categories according to their inherent capacity levels. The high capacity A cells are commonly sold for special applications at premium prices; the large mid-range B cells are used for commercial and industrial applications such as mobile communications; and the low-end C cells are mostly sold in supermarkets at bargain prices. Cycling will not significantly improve the capacity of the low-end cell. When purchasing rechargeable batteries at a reduced price, the buyer should be aware of the different capacity and quality levels offered.

14. Non-Correctable Battery Problems 3

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14.4 Shorted Cells

Manufacturers are often unable to explain why some cells develop high electrical leakage or an electrical short while the batteries are still relatively new. There are a number of possible reasons that contribute to this irreversible form of cell failure.

The suspected culprit is foreign particles that contaminate the cells during manufacture. Another possible cause is rough spots on the plates that damage the separator. Better quality control at the raw material level and minimal human interface during the manufacturing process has greatly reduced the ‘infant mortality’ rate of the modern rechargeable cells.

14. Vector Space Concepts

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Vector Space Concepts
Definition. A set of objects is called a metric spaceif with any two points and of there is associated a real number, called the distance from to , such that (a) if ; , (b) , (c) , for any [Rudin 1964].

15. Bibliography

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Bibliography
Crochiere and Rabiner 1983
Crochiere, R., and L. R. Rabiner. 1983.
Multirate Digital Signal Processing.
Englewood Cliffs, NJ: Prentice-Hall, Inc.
Digital Signal Processing Committee 1979a
Digital Signal Processing Committee (ed). 1979a.
Programs for Digital Signal Processing.
New York: IEEE Press.

15. Caring for Your Batteries from Birth to Retirement

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15. Caring for Your Batteries from Birth to Retirement
It is interesting to observe that batteries cared for by a single user generally last longer than those that operate in an open fleet system where everyone has access to, but no one is accountable for them. There are two distinct groups of battery users — the personal user and the fleet operator.
A personal user is one who operates a mobile phone, a laptop computer or a video camera for business or pleasure. He or she will most likely follow the recommended guidelines in caring for the battery. The user will get to know the irregularities of the battery. When the runtime gets low, the battery often gets serviced or replaced. Critical failures are rare because the owner adjusts to the performance of the battery and lowers expectations as the battery ages.

15. Caring for Your Batteries from Birth to Retirement 2

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15.1 Storage

Batteries are a perishable product and start deteriorating right from the time they leave the manufacturing plant. For this reason, it is not advisable to stock up on batteries for future use. This is especially true with lithium-based batteries. The buyer should also be aware of the manufacturing date. Avoid acquiring old stock.

Keep batteries in a cool and dry storage area. Refrigerators are recommended, but freezers must be avoided because most battery chemistries are not suited for storage in sub-freezing temperatures. When refrigerated, the battery should be placed in a plastic bag to protect it against condensation.

15. Caring for Your Batteries from Birth to Retirement 3

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15.2 Priming

Some nickel-based batteries do not perform well when new. This deficiency is often caused by lack of formatting at the time of manufacturing. Batteries that are not sufficiently formatted are destined to fail because the initial capacity is low. The full potential is only reached after the battery has been cycled a few times. In many cases, the user does not have the patience to wait until the expected performance is reached. Instead, the customer exercises the warranty return option.

15. Caring for Your Batteries from Birth to Retirement 4

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15.3 The Million Dollar Battery Problem

In today’s surging mobile phone market, many batteries are returned to mobile phone carriers before the ink on the invoice has dried. The most common consumer complaint is ‘less than expected’ runtime.

The reasons for this failure are multi-fold. The battery may not have been properly formatted at the factory. Perhaps the packs remained on the shelf too long or have been discharged too low. Incorrect customer preparation is also to blame. The true reason for such failure may never be known.

15. Caring for Your Batteries from Birth to Retirement 5

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15.4 To the Service Counter, and No Further

Not all manufacturers and dealers offer battery-refurbishing centers. If not available, a program is gaining popularity in which the battery is serviced at the store level. When a customer returns a faulty battery, the pack goes no further than the store that sold the equipment.

The customer service clerk checks the battery on site with approved test equipment. An attempt is made to restore the battery. If not successful and a warranty replacement is needed, a service report is issued, which is sent to the manufacturer by fax or e-mail. After verifying the report, the manufacturer offers replacement batteries as part of the warranty replacement policy.

15. Caring for Your Batteries from Birth to Retirement 6

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15.5 The Quick Fix

Checking a battery and assessing its status within a few minutes is one thing — finding a solution and actually fixing the problem is another. Increasingly, customers and dealers alike are seeking an alternative solution to replacing the batteries under warranty. They want a quick fix.

Fully automated test procedures are being developed which check the battery and apply a quick-prime program to wake up a sleeping battery. The program will last from a few minutes for an easy wake-up call, to an hour or longer for the deep-sleepers.

15. Caring for Your Batteries from Birth to Retirement 7

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15.6 Battery Warranty

Some manufacturers of industrial batteries provide warranties of up to 18 months. A free exchange is offered if the battery fails to meet 80 percent of the rated capacity throughout the warranty period. (I hasten to mention that these warranty policies apply to markets other than mobile phones.)

But what happens if such a battery is returned for warranty? Will the dealer replace the pack without hesitation? Rarely.

15. Caring for Your Batteries from Birth to Retirement 8

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15.7 Battery Recycling

Even though the emphasis in battery research has shifted away from NiCd to newer technologies, the NiCd battery continues to be one of the most used rechargeable batteries. Over 75 million NiCd batteries were sold in the US during the year 2000. Market reports indicate that the demand of NiCd batteries is expected to rise six percent per year until 2003. The demand for other chemistries, such as the NiMH and Li-ion family, is rising at a more rapid pace. Where will the mountains of batteries go when spent? The answer is recycling.

15. Specific Norms

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Specific Norms
The norms are defined on the space by

16. About this document

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About this document
This document is a new HTML formatted version published by permission of:

The Digital Audio Resampling Home Page by Julius O. Smith III, Last updated January 17, 2000.
Julius O. Smith III, Ph.D. Dissertation, Center for Computer Research in Music and Acoustics (CCRMA), Department of Electrical Engineering, Stanford University, June 1983...

Copyright © 2000-09-19 by Julius O. Smith III

16. Concavity (Convexity)

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Concavity (Convexity)
Definition. A set is said to be concave if for every vector and in , is in for all . In other words, all points on the line between two points of lie in .

16. Practical Battery Tips

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16. Practical Battery Tips
Batteries seem to have a mind of their own. Their stubborn and unpredictable behavior has left many battery users in awkward situations. In fact, the British Army could have lost the Falkland War in 1982 because of uncooperative batteries. The army assumed that a battery would always follow rigid military specifications. Not so. When the order was given to launch the portable missiles, nothing happened and the missiles did not fly that day. Such battery-induced letdowns happen on a daily basis. Some are simply a nuisance, others have serious consequences.

16. Practical Battery Tips 2

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16.2 The Correct Battery for the Job

What is the best battery choice? The requirements differ between personal users and fleet operators. The personal user can choose batteries in various sizes and chemistries. Cost is a factor for many. If a smaller and less energy-dense battery is chosen, a spare battery may be carried to assure continued service.

The energy requirements are quite different with fleet operators. The equipment is matched with a battery designed to run for a specified number of hours per shift. A degradation factor to compensate for battery aging is taken into account. A reserve capacity is added to allow for unforeseen activities. Allowing an aging degradation factor of 20 percent and providing a reserve capacity of 20 percent will reduce the usable battery capacity from 100 percent to 60 percent in a worst-case scenario. Such a large percentage of reserve capacity may not always be practical but the equipment manufacturers should consider these safety factors when fitting the portable devices with a battery.

16. Practical Battery Tips 3

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16.3 Battery Analyzers for Critical Missions

Occasionally, a customer will call Cadex because their battery analyzer appears faulty. The complaint: the battery no longer indicates correct capacity readings. In most cases, the customer has just purchased new batteries. When testing these new packs, the capacities read 50 to 70 percent. The customer assumes that, “Naturally, if two or more of these brand new batteries show low readings, it can only be the analyzer’s fault.”

17. Concave Norms

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Concave Norms
A desirable property of the error norm minimized by a filter-designtechnique is concavity of the error norm with respect to the filter coefficients. When this holds, the error surface ``looks like a bowl,'' and the global minimumcan be found by iteratively moving the parameters in the ``downhill'' (negative gradient) direction. The advantages of concavity are evident from the following classical results.

17. Did you know . . . ?

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17. Did you know . . . ?
Technological advancements usually take off shortly after a major breakthrough has occurred. Electricity was discovered circa 1600 AD (or earlier). At that time, electric power had few other applications than creating sparks and experimenting with twitching frog legs. Once the relationship with magnetism was discovered in the mid 1800s, generators were invented that produced a steady flow of electricity. Motors followed that enabled mechanical movement and the Edison light bulb was invented to conquer the dark.

17. Did you know . . . ? 2

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17.1 The Cost of Mobile Power

Among the common power sources, energy from non-rechargeable batteries is the most expensive. Figure 17-1 reflects the cost per kWh using non-rechargeable batteries, also referred to as primary batteries. In addition, non-rechargeable batteries have a high internal cell resistance, which limits their use to light loads with low discharge currents.

In the last few decades, there has been a shift from non-rechargeable to rechargeable batteries, also known as secondary batteries. The convenience of recharging, low cost and reliable operation have contributed to this. Another reason for the increased popularity of the secondary battery is the larger energy densities available. Some of the newer rechargeable lithium systems now approach or exceed the energy density of a primary battery.

17. Did you know . . . ? 3

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17.2 The Fuel Cell

A fuel cell is an electrochemical device which combines hydrogen fuel with oxygen to produce electric power, heat and water. In many ways, the fuel cell resembles a battery. Rather than applying a periodic recharge, a continuous supply of oxygen and hydrogen is supplied from the outside. Oxygen is drawn from the air and hydrogen is carried as a fuel in a pressurized container. As alternative fuel, methanol, propane, butane and natural gas can be used.

17. Did you know . . . ? 4

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Types of fuel cells — Several variations of fuel cell systems have emerged. The most common are the previously mentioned and most widely developed PEMFC systems using a polymer electrolyte. This system is aimed at vehicles and portable electronics. Several developers are also targeting stationary applications. The alkaline system, which uses a liquid electrolyte, is the preferred fuel cell for aerospace applications, including the space shuttle. Molten carbonate, phosphoric acid and solid oxide fuel cells are reserved for stationary applications, such as power generating plants for electric utilities. Among these stationary systems, the solid oxide fuel cell system is the least developed but has received renewed attention due to breakthroughs in cell material and stack designs.

17. Did you know . . . ? 5

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Applications — The fuel cell is being considered as an eventual replacement for the internal combustion engine for cars, trucks and buses. Major car manufacturers have teamed up with fuel cell research centers or are doing their own development. There are plans for mass-producing cars running on fuel cells. However, because of the low operating cost of the combustion engine, and some unresolved technical challenges of the fuel cell, experts predict that a large scale implementation of the fuel cell to power cars will not occur before 2015, or even 2020.

17. Did you know . . . ? 6

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17.3 The Electric Vehicle

In a bid to lower air pollution in big cities, much emphasis has been placed on the electric car. The notion of driving a clean, quiet and light vehicle appeals to many city dwellers. Being able to charge the car at home for only a dollar a day and escape heavy fuel taxes (at least for the time being) makes the electric car even more attractive.

17. Footnotes

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Footnotes
... kHz.¹
We arbitrarily define the % guard band as a percentage of half the sampling rate actually used, not as % of the desired kHz bandwidth which would call for a kHz sampling rate.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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18. Beginnings and Horizons

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18. Beginnings and Horizons
18.1 About the Author

A versatile inventor, researcher and writer, Mr. Isidor Buchmann is the president, founder and CEO of Cadex Electronics Inc., located in Richmond (Vancouver), Canada.

Fascinated by electronics during his high school years, Mr. Buchmann took to inventing at an early age, designing a fuel-powered engine that was based on continuous combustion. His drawings and theory of operation were reviewed by Felix Wankel, inventor of the Wankel Rotary Engine, who kindly replied that while the design was indeed unique and original, manufacturing would be too expensive to be commercially viable. Further to his credit, Mr. Buchmann invented a broadcast radio that ran on no power — it required only an antenna and a ground connection (it didn’t even use a battery). Mr. Buchmann sold several of these radio receivers to his family and colleagues and later set up a workshop in the attic where he restored and resold old radios. After high school, a four-year apprenticeship as a Radio Technician brought him practical experience in a workshop environment as well as academic theory. Finally, his experience with radio communications in the Swiss army led to his decision to make electronics his life's work.

18. Beginnings and Horizons 2

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18.2 About Cadex

Cadex Electronics Inc. was established in 1980 in Vancouver, Canada. Isidor Buchmann, founder, president and CEO recognized that the full potential of nickel cadmium batteries was not being achieved and developed a battery analyzer to exercise and rejuvenate them.

In its early days, the company operated under the name Buchmann Enterprises Inc. Until 1983, all activities were conducted in a small room of the founder’s residence. In 1985, after the registered trademark for the name ‘Cadex’ was granted, the company changed the corporate name to Cadex Electronics Inc. Cadex is derived from ‘CADmium-EXerciser.’

18. Beginnings and Horizons 3

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18.3 Working with Natural Beauty

The new Cadex headquarters is nestled in natural surroundings. The scenic Fraser River lies to the south, a public park to the east and the Coastal Mountains to the north. For joggers and cyclists, there is a nature path between the building and the river.

The interior of the building is designed with employee comfort in mind. It includes a snooker table, a gym, shower rooms, and several televisions. Balconies with a river view overlook the outdoor patio, which is used for summer lunches.

18. Beginnings and Horizons 4

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18.5 Cadex Products

Cadex products are built with one goal in mind — to make batteries run longer. Cadex has realized the importance of battery care and is offering equipment to charge, test, monitor, and restore batteries.

Cadex’s core competence is engineering. Over 25 percent of the Cadex staff is active in the Engineering Department. Existing products are improved on a continual basis, and new and creative products are added to adjust to the changing demands of battery users. Key products include:

18. Beginnings and Horizons 5

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Cadex Batteryshop™ software provides a simple, yet powerful PC interface to control and monitor the Cadex 7000 Series battery analyzers. Running on Windows 95, 98 and NT, the software enables untrained staff to test batteries as part of customer service. In addition, Cadex Batteryshop™ schedules periodic maintenance for fleet owners and assists battery manufacturers with quality control.

Cadex Batteryshop™ includes a database of over 2000 common battery models. Each battery listing contains the configuration code (C-code), the data that sets the analyzer to the correct parameters. A growing number of the battery listings also include matrices to perform Cadex Quicktest™.

18. Gradient Descent

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Gradient Descent
Concavity is valuable in connection with the Gradient Method of minimizing with respect to .
Definition. The gradient of the error measure is defined as the column vector

19. Taylor's Theorem

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Taylor's Theorem
Theorem. (Taylor) Every functional in has the representation

2. A CLOSER LOOK

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2. A CLOSER LOOK
2.1. WHAT MEMORY LOOKS LIKE
2.2. WHERE MEMORY COMES FROM
2.3. WHERE MEMORY GOES IN THE COMPUTER
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2. Principles of ESD Control

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2. Principles of ESD Control
In Part One, we discussed the basics of electrostatic charge, discharge, types of failures, ESD events, and device sensitivity. We summarized this discussion as follows:

Virtually all materials, even conductors, can be triboelectrically charged.
The level of charge is affected by material type, speed of contact and separation, humidity, and several other factors.
Electrostatic discharge can create catastrophic or latent failures in electronic components.
Electrostatic discharge can occur throughout the manufacturing, test, shipping, handling, or operational processes.
Component damage can occur as the result of a discharge from the component as well as a direct discharge to the component.
Components vary significantly in their sensitivity to ESD.
With this basic understanding of ESD and its impact on your environment, you can then begin to develop an effective ESD control program. In this column and the next, we will focus on basic Principles of ESD control.

2.1. WHAT MEMORY LOOKS LIKE

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2.1. WHAT MEMORY LOOKS LIKE
Memory comes in a variety of sizes and shapes. In general, it looks like a flat green stick with little black cubes on it. Obviously, there's a lot more to memory than that. The illustration below shows a typical memory module and points out some of its most important features.

A closer look at a 168-pin SDRAM DIMM.

2.2. WHERE MEMORY COMES FROM

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2.2. WHERE MEMORY COMES FROM
MAKING THE CHIP
Amazing but true: memory starts out as common beach sand. Sand contains silicon, which is the primary component in the manufacture of semiconductors, or "chips." Silicon is extracted from sand, melted, pulled, cut, ground, and polished into silicon wafers. During the chip-making process, intricate circuit patterns are imprinted on the chips through a variety of techniques. Once this is complete, the chips are tested and die-cut. The good chips are separated out and proceed through a stage called "bonding": this process establishes connections between the chip and the gold or tin leads, or pins. Once the chips are bonded, they're packaged in hermetically sealed plastic or ceramic casings. After inspection, they're ready for sale.

2.3. WHERE MEMORY GOES IN THE COMPUTER

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2.3. WHERE MEMORY GOES IN THE COMPUTER
Originally, memory chips were connected directly to the computer's motherboard or system board. But then space on the board became an issue. The solution was to solder memory chips to a small modular circuit board - that is, a removable module that inserts into a socket on the motherboard. This module design was called a SIMM (single in-line memory module), and it saved a lot of space on the motherboard. For example, a set of four SIMMs might contain a total of 80 memory chips and take up about 9 square inches of surface area on the motherboard. Those same 80 chips installed flat on the motherboard would take up more than 21 square inches on the motherboard.

These days, almost all memory comes in the form of memory modules and is installed in sockets located on the system motherboard. Memory sockets are easy to spot because they are normally the only sockets of their size on the board. Because it's critical to a computer's performance for information to travel quickly between memory and the processor(s), the sockets for memory are typically located near the CPU.

20. Newton's Method

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Newton's Method
The gradient method is based on the first-order term in the Taylor expansion for . By taking a second-order term as well and solving the quadratic minimization problem iteratively, Newton's method for functional minimization is obtained. Essentially,Newton's method requires the error surface to be close toquadratic, and its effectiveness is directly tied to the accuracy of this assumption. For most problems, the error surface can be well approximated by a quadratic form near the solution. For this reason, Newton's method tends to give very rapid (``quadratic'') convergence in the last stages of iteration.

21. Maxims of Signal Processing

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Maxims of Signal Processing
Every technique is equivalent to the same operation, once you really understand it.
If one technique is superior to another, it is due to more averaging.

22. Index

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Index
-transform
Convolution Representation
norms
Specific Norms
norms
Specific Norms
amplitude response
Frequency Response | Frequency Response
Banach Space
Vector Space Concepts
Cauchy sequence
Vector Space Concepts
causal
Difference Equation | Specific Norms
Chebyshev norm
Specific Norms
cluster point
Concavity (Convexity)
concave
Concavity (Convexity)
concave error surface
Concave Norms
concave functional
Concavity (Convexity)
concave hull
Concavity (Convexity)
convergence, existence of minimizer
Concave Norms
convergence, global
Concave Norms
difference equation
Difference Equation
difference equation coefficients
Difference Equation
filter
Introduction to Digital Filter
filter coefficients
Difference Equation
filter delay for amplitude envelopes
Phase Delay and Group
filter order
Difference Equation
filter power response
Frequency Response
filter time delay
Phase Delay and Group
frequency response
Frequency Response
Frobenious norm
Specific Norms
functional
Concavity (Convexity)
global convergence, conditions for
Concave Norms
global minimizer
Concavity (Convexity)
gradient
Gradient Descent
Gradient Method
Gradient Descent
group delay
Phase Delay and Group
Hankel matrix
Specific Norms
Hankel norm
Specific Norms
Hessian
Gradient Descent
impulse
Difference Equation
impulse response
Difference Equation
induced norm
Specific Norms
linear
Linearity and Time-Invariance
linear filter
Linearity and Time-Invariance
linear functional
Concavity (Convexity)
linear space
Vector Space Concepts
local minimizer
Concavity (Convexity)
LTI filters
Linearity and Time-Invariance
metric space
Vector Space Concepts
Newton's method
Newton's Method
norm
Vector Space Concepts
normed linear space
Vector Space Concepts
outer disk
Positive Real Functions
phase delay
Phase Delay and Group
phase response
Frequency Response | Frequency Response
phase response at zero frequency
Phase Delay and Group
positive real
Positive Real Functions
pseudo-norm
Vector Space Concepts
real filter
Difference Equation
root mean square norm
Specific Norms
Schur function
Relation to Schur Functions
signal
Introduction to Digital Filter
spectral norm
Specific Norms
stable
Difference Equation
stationary point
Gradient Descent
strictly concave functional
Concavity (Convexity)
time-invariant
Linearity and Time-Invariance
transfer function
Convolution Representation
uniform norm
Specific Norms
uniformly concave
Concavity (Convexity)
weighted norms
Specific Norms
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23. Bibliography

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Bibliography
Astrom 1970
Astrom, K. J. 1970.
Introduction to Stochastic Control Theory.
New York: Academic Press.
Brune 1931
Brune, O. 1931.
``Synthesis of a finite two terminal network whose driving point impedance is a prescribed function of frequency.''
Pages 191-236 of: J. Math. and Phys., vol. 10.

24. About this document

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"Elementary Digital Filter Theory" by Julius O. Smith III,
Adpated from "Techniques for Digital FilterDesign and System Identification, with Application to the Violin",
Julius O. Smith III, Ph.D. Dissertation, Center for Computer Research in Music and Acoustics (CCRMA), Department of Electrical Engineering, Stanford University, June 1983...

Copyright © 2000-09-19 by Julius O. Smith III

25. Footnotes

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Introduction to Digital Filters with Audio Applications", by Julius O. Smith III, Copyright © 2017-11-26 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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3. An Overview of ESD Control Procedures and Materials

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3. An Overview of ESD Control Procedures and Materials
In Part Two---Principles of ESD Control we introduced four principles of static control and nine key elements of ESD program development and implementation. In Part Three, we will cover some of the primary specific static control procedures and materials that become part of your program. First, a quick review.
Basic Principles of Static Control
We suggested that static control programs become more effective and less complex if we focus on just four basic principles of static control as follows:

3. HOW MEMORY WORKS

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3. HOW MEMORY WORKS
Earlier, we talked about how memory holds information in a place where the CPU can get to it quickly. Let's look at that process in more detail.

3.1. HOW MEMORYWORKS WITH THE PROCESSOR
3.2. MAXIMIZING PERFORMANCE
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3.1. HOW MEMORYWORKS WITH THE PROCESSOR

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3.1. HOW MEMORYWORKS WITH THE PROCESSOR

Main components of a computer system.
The CPU is often referred to as the brain of the computer. This is where all the actual computing is done.
The chipset supports the CPU. It usually contains several "controllers" which govern how information travels between the processor and other components in the system. Some systems have more than one chipset.

3.2. MAXIMIZING PERFORMANCE

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3.2. MAXIMIZING PERFORMANCE
Computer processor speeds have been increasing rapidly over the past several years. Increasing the speed of the processor increases the overall performance of the computer. However, the processor is only one part of the computer, and it still relies on other components in a system to complete functions. Because all the information the CPU will process must be written to or read from memory, the overall performance of a system is dramatically affected by how fast information can travel between the CPU and main memory.

So, faster memory technologies contribute a great deal to overall system performance. But increasing the speed of the memory itself is only part of the solution. The time it takes for information to travel between memory and the processor is typically longer than the time it takes for the processor to perform its functions. The technologies and innovations described in this section are designed to speed up the communication process between memory and the processor.

4. Auditing and Training

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4. Auditing and Training
Your static control program is up and running. How do you determine whether it is effective? How do you make sure your employees follow it? Previously, we suggested that there were at least nine critical elements to successfully developing and implementing an effective ESD control program. In Part Four, we will focus on two more of these elements: training and auditing.
Personnel Training

4. HOW MUCH MEMORY IS ON A MODULE?

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4. HOW MUCH MEMORY IS ON A MODULE?
Up to now, we've discussed some of the technical attributes of memory and how memory functions in a system. What's left are the technical details - the "bits and bytes," as they say. This section covers the binary numbering system, which forms the basis of computing, and calculation of a memory module's capacity.

4.1. BITS AND BYTES
4.2. CPU AND MEMORY REQUIREMENTS
4.3. CALCULATING THE CAPACITY OF A MODULE
4.4. STACKING

4.1. BITS AND BYTES

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4.1. BITS AND BYTES
Computers speak in a "code" called machine language, which uses only two numerals: 0 and 1. Different combinations of 0s and 1s form what are called binary numbers. These binary numbers form instructions for the chips and microprocessors that drive computing devices - such as computers, printers, hard disk drives, and so on. You may have heard the terms "bit" and "byte." Both of these are units of information that are important to computing. The term bit is short for "binary digit." As the name suggests, a bit represents a single digit in a binary number; a bit is the smallest unit of information used in computing and can have a value of either 1 or a 0. A byte consists of 8 bits. Almost all specifications of your computer's capabilities are represented in bytes. For example, memory capacity, data-transfer rates, and data-storage capacity are all measured in bytes or multiples thereof (such as kilobytes, megabytes, or gigabytes).

This discussion of bits and bytes becomes very relevant when it comes to computing devices and components working together. Here, we'll address specifically how bits and bytes form the basis of measuring memory component performance and interaction with other devices like the CPU.

4.2. CPU AND MEMORY REQUIREMENTS

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4.2. CPU AND MEMORY REQUIREMENTS
A computer's CPU (central processing unit) processes data in 8-bit chunks. Those chunks, as we learned in the previous section, are commonly referred to as bytes. Because a byte is the fundamental unit of processing, the CPU's processing power is often described in terms of the maximum number of bytes it can process at any given time. For example, Pentium and PowerPC microprocessors currently are 64-bit CPUs, which means they can simultaneously process 64 bits, or 8 bytes, at a time.

Each transaction between the CPU and memory is called a bus cycle. The number of data bits a CPU can transfer during a single bus cycle affects a computer's performance and dictates what type of memory the computer requires. Most desktop computers today use 168-pin DIMMs, which support 64-bit data paths. Earlier 72-pin SIMMs supported 32-bit data paths, and were originally used with 32-bit CPUs. When 32-bit SIMMs were used with 64-bit processors, they had to be installed in pairs, with each pair of modules making up a memory bank. The CPU communicated with the bank of memory as one logical unit.

Interestingly, RIMM modules, which are newer than DIMMs, use smaller 16-bit data paths; however they transmit information very rapidly, sending several packets of data at a time. RIMM modules use pipelining technology to send four 16-bit packets at a time to a 64-bit CPU, so information still gets processed in 64-bit chunks.

4.3. CALCULATING THE CAPACITY OF A MODULE

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4.3. CALCULATING THE CAPACITY OF A MODULE
Memory holds the information that the CPU needs to process. The capacity of memory chips and modules are described in megabits (millions of bits) andmegabytes (millions of bytes). When trying to figure out how much memory you have on a module, there are two important things to remember:

A module consists of a group of chips. If you add together the capacities of all the chips on the module, you get the total capacity of the module. Exceptions to this rule are:

If some of the capacity is being used for another function, such as error checking.

If some of the capacity is not being used, for example some chips may have extra rows to be used as back-ups. (This isn't common.)
While chip capacity is usually expressed in megabits, module capacity is expressed in megabytes. This can get confusing, especially since many people unknowingly use the word "bit" when they mean "byte" and vice versa. To help make it clear, we'll adopt the following standards in this book:

When we talk about the amount of memory on a module, we'll use the term "module capacity"; when we are referring to chips, we'll use the term "chip density". Module capacity will be measured in megabytes (MB) with both letters capital, and chip density will be measured in megabits (Mbit), and we'll spell out the word "bit" in small letters.

4.4. STACKING

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4.4. STACKING

Many large servers and workstations require higher capacity modules in order to reach system memory capacities of several gigabytes or more. There are two ways to increase the capacity of a module. Manufacturers can stack chips on top of one another, or they can stack boards.
CHIP STACKING

With chip stacking, two chips are stacked together and occupy the space that one chip would normally take up. In some cases, the stacking is done internally at the chip manufacturing plant and can actually appear to be one chip. In other cases the chips are stacked externally. The example below shows two externally stacked chips.

Example of externally stacked chips.

5. Device Sensitivity and Testing

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5. Device Sensitivity and Testing
In Part Two, we indicated that one of the key elements in a successful static control program was the identification of those items (components, assemblies, and finished products) that are sensitive to ESD and the level of their sensitivity. Damage to an ESDS device by the ESD event is determined by the device's ability to dissipate the energy of the discharge or withstand the current levels involved. This is known as device "ESD sensitivity" or "ESD susceptibility".

5. DIFFERENT KINDS OF MEMORY

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5. DIFFERENT KINDS OF MEMORY
Some people like to know a lot about the computer systems they own - or are considering buying - just because. They're like that. It's what makes them tick. Some people never find out about their systems and like it that way. Still other people - most of us, in fact - find out about their systems when they have to - when something goes wrong, or when they want to upgrade it. It's important to note that making a choice about a computer system - and its memory features - will affect the experience and satisfaction you derive from the system. This chapter is here to make you smarter about memory so that you can get more out of the system you're purchasing or upgrading.

5.1. MODULE FORM FACTORS
5.2. MAJOR CHIP TECHNOLOGIES
5.3. MEMORY TECHNOLOGIES FOR VIDEO OR GRAPHICS PROCESSING
5.4. OTHER MEMORY TECHNOLOGIES YOU MAY HAVE HEARD ABOUT
5.5. ERROR CHECKING
5.6. OTHER SPECIFICATIONS

5.1. MODULE FORM FACTORS

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5.1. MODULE FORM FACTORS
The easiest way to categorize memory is by form factor. The form factor of any memory module describes its size and pin configuration. Most computer systems have memory sockets that can accept only one form factor. Some computer systems are designed with more than one type of memory socket, allowing a choice between two or more form factors. Such designs are usually a result of transitional periods in the industry when it's not clear which form factors will gain predominance or be more available.

5.2. MAJOR CHIP TECHNOLOGIES

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5.2. MAJOR CHIP TECHNOLOGIES
It's usually pretty easy to tell memory module form factors apart because of physical differences. Most module form factors can support various memory technologies so, it's possible for two modules to appear to be the same when, in fact, they're not. For example, a 168-pin DIMM can be used for EDO, Synchronous DRAM, or some other type of memory. The only way to tell precisely what kind of memory a module contains is to interpret the marking on the chips. Each DRAM chip manufacturer has different markings and part numbers to identify the chip technology.

5.3. MEMORY TECHNOLOGIES FOR VIDEO OR GRAPHICS PROCESSING

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5.3. MEMORY TECHNOLOGIES FOR VIDEO OR GRAPHICS PROCESSING
VIDEO RAM (VRAM)
VRAM is a video version of FPM technology. VRAM typically has two ports instead of one, which allows the memory to allocate one channel to refreshing the screen while the other is focused on changing the images on the screen. This works much more efficiently than regular DRAM when it comes to video applications. However, since video memory chips are used in much lower quantities than main memory chips, they tend to be more expensive. So, a system designer may choose to use regular DRAM in a video subsystem, depending on whether cost or performance is the design objective.

5.4. OTHER MEMORY TECHNOLOGIES YOU MAY HAVE HEARD ABOUT

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5.4. OTHER MEMORY TECHNOLOGIES YOU MAY HAVE HEARD ABOUT
ENHANCED SDRAM (ESDRAM)
In order to increase the speed and efficiency of standard memory modules, some manufacturers have incorporated a small amount of SRAM directly into the chip, effectively creating an on-chip cache. ESDRAM is essentially SDRAM, plus a small amount of SRAM cache, which allows for burst operations of up to 200MHz. Just as with external cache memory, the goal of cache DRAM is to hold the most frequently used data in the SRAM cache to minimize accesses to the slower DRAM. One advantage of on-chip SRAM is that it enables a wider bus between the SRAM and DRAM, effectively increasing the bandwidth and speed of the DRAM.

5.5. ERROR CHECKING

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5.5. ERROR CHECKING
Ensuring the integrity of data stored in memory is an important aspect of memory design. Two primary means of accomplishing this are parity and error correction code (ECC).

Historically, parity has been the most commonly used data integrity method. Parity can detect - but not correct - single-bit errors. Error Correction Code (ECC) is a more comprehensive method of data integrity checking that can detect and correct single-bit errors.

Fewer and fewer PC manufacturers are supporting data integrity checking in their designs. This is due to a couple of factors. First, by eliminating support for parity memory, which is more expensive than standard memory, manufacturers can lower the price of their computers. Fortunately, this trend is complemented by the second factor: that is, the increased quality of memory components available from certain manufacturers and, as a result, the relative infrequency of memory errors.

The type of data integrity checking depends on how a given computer system will be used. If the computer is to play a critical role - as a server, for example - then a computer that supports data integrity checking is an ideal choice. In general:

Most computers designed for use as high-end servers support ECC memory.
Most low-cost computers designed for use at home or for small businesses support non-parity memory.

5.6. OTHER SPECIFICATIONS

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5.6. OTHER SPECIFICATIONS
In addition to form factors, memory technologies, and error checking methods, there are several other specifications important to understanding and selecting memory products.
SPEED
The speed of memory components and modules is one of the most important factors in optimizing a memory configuration. In fact, all computer systems specify a memory component speed. Ensuring memory compatibility requires conforming to this specification. This section covers three measurements of memory component and module speed: access time, megahertz, and bytes per second.

6. ESD Standards

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6. ESD Standards
In a world that is characterized by change, the ESD industry seems to have jumped into the swirling eddy head-first. Control programs have mushroomed. Black has been replaced by green, blue and gold. Shielding bags dominate the warehouse. Ionizers exist along side wrist straps and ground cords. An early history of "smoke and mirrors," magic and lofty claims of performance is rapidly and safely being relegated to the past.

6. WHAT TO CONSIDER WHEN BUYING MEMORY

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6. WHAT TO CONSIDER WHEN BUYING MEMORY
One of the quickest and easiest ways to identify the right memory modules and expansion options for your computer is to use a memory configurator. Like some of the other major memory manufacturers, Kingston makes a memory configurator available. You can access Kingston's configurator through their home page at www.kingston.com.

The most important thing to ensure when buying memory is compatibility with your system. In addition, you'll need to decide how much memory you need and beyond that lie considerations of price, quality, availability, service, and warranty. This section helps you address these important decision factors and helps you answer questions like these:

How much memory do I need?
How much memory will my system recognize?
What kind of memory is compatible with my system?
How many sockets are open and how should I fill them?
How do I determine the quality of memory?
What should I know about memory prices?
What other issues should I consider?

6.1. COMPATIBILITY
6.2. HOW TO READ A BANK SCHEMA
6.3. QUALITY
6.4. PRICING AND AVAILABILITY

6.1. COMPATIBILITY

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6.1. COMPATIBILITY
As mentioned earlier, compatibility of memory components with your computer system is arguably the most important factor to consider when upgrading memory. This section can get you started; it also makes frequent mention of the advantages of using a memory configurator.
WHAT KIND OF MEMORY IS COMPATIBLE WITH MY SYSTEM?
The easiest way to determine what type of memory goes with your system is to consult with your system documentation. If you need further assistance, consult a memory configurator available from many sources, including Kingston. Kingston and other brand-name memory companies offer such a tool to help you find the right memory configuration for your system.

With Kingston's configurator, you can search by five different criteria:

System manufacturer/model
Computer model name
Memory module part number (Kingston, distributor, manufacturer)
Specification
Generic memory
To access Kingston's Memory Configurator, click here

6.2. HOW TO READ A BANK SCHEMA

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6.2. HOW TO READ A BANK SCHEMA
A bank schema is a diagram of rows and columns that shows the number of memory sockets in your system. This diagram is a theoretical bank layout and not an actual system board layout; it is designed to help you quickly determine configuration requirements when adding memory modules.

In a bank schema, each represents a memory socket:

Example: = 4 memory sockets

Each column in the diagram represents a memory bank. The number of " " symbols in a column represents the number of memory sockets in a bank. Upgrading is performed one bank at a time. For example, if there are four columns with two in each column, upgrading is done two modules at a time. However, if there is just a single row of , upgrading may be performed one module at a time.

Examples:

8 sockets =
(Modules may be installed one at a time in any combination)

8 sockets (4 banks of 2) =

(Modules must be installed two at a time)

4 sockets (1 bank of 4) =

(Modules must be installed four
at a time)

The standard memory (base amount that the system was shipped with) appears in the diagram as either removable or non-removable.

Removable memory comes in the form of modules that fit into memory sockets, and, if desired, can be removed and replaced with modules of higher capacity. Removable memory is represented by a "" symbol with a number next to it: 4 that a 4MB module is in the first socket and that the second socket is empty.

Non-removable memory usually comes in the form of memory chips soldered directly onto the system board. It is represented in the bank schema in brackets: [_4MB_] indicates 4MB of non-removable memory soldered onto the board and two available memory sockets.

If your system is not included in the configurator, you may be able to find out how many sockets are in the system and how many are filled by pressing the F1 key during system startup. If your system supports this, a screen will appear that indicates how many memory sockets are in the system, which ones are filled and which are open, and what capacity modules are in each socket. If pressing the F1 key during startup doesn't produce this result, check your computer's system manual for more information.

As a last resort, you can open your computer and take a look at the sockets. (Important Note: Before removing the cover of your computer, refer to the computer's system manual and warranty information for instructions and other relevant information.) If you do open the computer, you may be able to identify "bank labels" that indicate whether memory are installed in pairs. Bank numbering typically begins with 0 instead of 1. So, if you have two banks, the first bank will be labeled "bank 0", and the second bank will be labeled "bank 1."

6.3. QUALITY

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6.3. QUALITY
As with any type of product, memory can vary in the quality from one manufacturer to another. In general, the larger, more established brand name companies are more consistent in adhering to tight design specifications, using high-quality components, and establishing certified quality control processes for manufacturing and thorough testing. That's not to say that lower-quality modules don't work fine - they may be the right solution, depending on how hard you work your system. In deciding the level of quality you require, consider the following:

If the memory you buy doesn't perform well, will you be comfortable returning it for a replacement? Would you have the time to deal with removing the memory and waiting a couple of days to a week to get the situation resolved?

When memory is of low quality, you often experience intermittent problems, such as the computer "freezing" unexpectedly, or having frequent errors. How often do you save your work, and if you were to lose your work, how much would that cost you? If you use your computer to play games, read email, and surf the Internet, such interruptions and losses may not be a big problem. But if you're running a business, losing a few hours of work could be a serious matter.

The biggest risk with unreliable memory is data corruption: that is, some bits of data may change or be read incorrectly. The result of data corruption could be as harmless as a syntax error in a document, or as potentially serious as a miscalculation in a spreadsheet. How important is the accuracy of the work you do on your computer? Again, if you use your computer for gaming, writing letters, and the Internet, it may not be a problem. But if you're managing your finances, you may want to do all you can to assure the reliability of your data.

Just like all products, the quality and durability you require depends on how you use it. Computer applications that require a lot of memory usually work the memory very hard. These applications often work better with memory that exceeds the system's speed and reliability specifications. If you're working in multimedia or using heavy number-crunching programs, the chance of a lower-quality memory module failing is greater than if you're only doing light work, such as simple word processing.

6.4. PRICING AND AVAILABILITY

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6.4. PRICING AND AVAILABILITY
This section contains information that helps make sense of the fluctuations that can occur in the memory market.

THE DRAM CHIP MARKET
Memory modules are made with DRAM chips, which are manufactured in mass quantities in enormous fabrication plants (often referred to as "fabs"). Fabs can take up to two years to build and require substantial capital investment: approximately $3 billion per plant. These time and cost factors directly affect on the ability of the memory market to adjust quickly to fluctuations in supply and demand. When demand for memory chips increases, chip manufacturers typically do not respond immediately because the investment required to add more capacity is substantial and may not pay off, especially if all the competitors are doing so at the same time. Therefore, the immediate effect is that prices rise as manufacturers assess whether the increase on demand is temporary or substantial enough to warrant investment. By the same token, when there is an oversupply situation in the market, chip manufacturers are willing to sustain losses for a long time while prices fall to below breakeven levels. This is because in many cases it costs more money to shut a plant down than to continue to produce and sell chips at below cost. Also, the longer a manufacturer can hold on, the greater the chance of "being there" to reap the rewards when competitors reduce capacity and the market turns around again.

7. Bibliography

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7. Bibliography
Key Device and Design Papers EOS/ESD Symposium Proceedings
The following list contains some of the most significant papers on silicon device ESD phenomena and protection design from past proceedings of the EOS/ESD Symposium. After a careful review, the papers were selected based on their original contribution to the field and their effectiveness in advancing the understanding of ESD device phenomena. These papers provide further understanding of the concepts as well as implementation and practical use. This collection of articles will allow new researchers interested in the field to quickly gather pertinent information. The papers are categorized according to the topic of interest. A brief statement on the significance of each paper also is provided.

7. HOW TO INSTALL MEMORY

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7. HOW TO INSTALL MEMORY
Congratulations! You have new memory for your computer. Now you have to install it. This chapter will guide you through the basics of memory module installation and refer you to resources that can help with problems.

7.1. BEFORE YOU INSTALL
7.2. IMPORTANT THINGS TO KEEP IN MIND
7.3. INSTALLING THE MEMORY
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7.1. BEFORE YOU INSTALL

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7.1. BEFORE YOU INSTALL
Before you start, make sure you have the following:
Your computer manual. To install memory, you must open the computer box (chassis) and locate the memory sockets. You may need to unplug cables and peripherals, and re-install them afterward. The manual will most likely provide instructions specific to your computer.

A small screwdriver. Most computer chassis assemble with screws. The screwdriver also comes in handy if the notches on memory sockets are too tiny for your fingers.

7.2. IMPORTANT THINGS TO KEEP IN MIND

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7.2. IMPORTANT THINGS TO KEEP IN MIND
ESD DAMAGE
Electro-Static Discharge (ESD) is a frequent causes of damage to the memory module. ESD is the result of handling the module without first properly grounding yourself and thereby dissipating static electricity from your body or clothing. If you have a grounded wrist strap, wear it. If you don't, before touching electronic components - especially your new memory module - make sure you first touch an unpainted, grounded metal object. Most convenient is the metal frame inside the computer. In addition, always handle the module by the edges. If ESD damages memory, problems may not show up immediately and may be difficult to diagnose.

Wearing a grounded wrist strap can prevent ESD damage.

7.3. INSTALLING THE MEMORY

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7.3. INSTALLING THE MEMORY
The vast majority of computers today have memory sockets that accept the following industry-standard memory modules:

Desktops, Workstations and Servers

72-pin SIMM
168-pin DIMM
184-pin RIMM
Notebooks and Mobile Computers

144-pin SO DIMM
Although sockets may be in different places on different computers, installation is the same. Consult the computer owner's manual to find out whether the memory sits on an expansion card or on the motherboard, and whether internal computer components must be moved to gain access.

In the section below are installation instructions for the standard modules listed above, followed by installation instructions for some of the more popular proprietary memory modules. If the computer requires proprietary memory, or the instructions below don't seem to apply to your situation, phone Kingston Technology's Technical Support Group at (800) 435-0640.

8. TROUBLESHOOTING MEMORY PROBLEMS

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8. TROUBLESHOOTING MEMORY PROBLEMS
8.1. COMMON MEMORY PROBLEMS
8.2. BASIC TROUBLESHOOTING
8.3. WHEN THE PROBLEM OCCURS
8.4. HANDLING SPECIFIC PROBLEMS
8.5. STILL NEED HELP?
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8.1. COMMON MEMORY PROBLEMS

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8.1. COMMON MEMORY PROBLEMS
When you have a problem with memory, the cause is usually one of three things:

Improper Configuration: You have the wrong part for your computer or did not follow the configuration rules.

Improper Installation: The memory may not be seated correctly, a socket is bad, or the socket may need cleaning.

Defective Hardware: The memory module itself is defective.

The fact that many computer problems manifest themselves as memory problems makes troubleshooting difficult. For example, a problem with the motherboard or software may produce a memory error message.

This chapter is designed to help you figure out if you have a memory problem, and if so, what kind of problem it is, so you can get to a solution as quickly as possible.

8.2. BASIC TROUBLESHOOTING

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8.2. BASIC TROUBLESHOOTING
The following basic steps apply to almost all situations:

Make sure you have the right memory part for your computer.At the manufacturer's Web site you can look up the part number. Many memory manufacturers have configurators, which indicate the compatibilities of your module. If not, phone the memory manufacturer, consult your computer manual, or phone the computer manufacturer.

Confirm that you configured the memory correctly.Many computers require module installation in banks of equal-capacity modules. Some computers require the highest capacity module to be in the lowest labeled bank. Other computers require that all sockets be filled; still others require single-banked memory. These are only a few examples of special configuration requirements. If you have a name-brand computer, visit Kingston's Web site (www.kingston.com) or use our upgrade manual to look up configuration rules specific to your computer. You can also contact technical support for your memory or computer manufacturer.

Re-install the module.Push the module firmly into the socket. In most cases you hear a click when the module is in position. To make sure you have a module all the way in the socket, compare the height of the module to the height of other modules in neighboring sockets.

Swap modules.Remove the new memory and see whether the problem disappears. Remove the old memory, reinstall the new, and see whether the problem persists. Try the memory in different sockets. Swapping reveals whether the problem is a particular memory module or socket, or whether two types of memory aren't compatible.

Clean the socket and pins on the memory module.Use a soft cloth to wipe the pins on the module. Use a PC vacuum or compressed air to blow dust off the socket. Do NOT use solvent, which may corrode the metal or prevent the leads from making full contact. Flux Off is a cleaner used specifically for contacts. You can purchase it at electronics or computer equipment stores.

Update the BIOS.Computer manufacturers update BIOS information frequently and post revisions on their Web sites. Make sure you have the most recent BIOS for your computer. This applies especially when you have recently installed new software or you are significantly upgrading memory.

8.3. WHEN THE PROBLEM OCCURS

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8.3. WHEN THE PROBLEM OCCURS
When the problem occurs is a clue as to the cause.

For example, your response to a memory error message depends on whether:

You have just bought a new computer.
You have just installed new memory.
You have just installed new software or a new operating system.
You have just installed or removed hardware.
Your computer has been running fine and you've made no other recent changes.

Here are rules to get started:

YOU'VE JUST BOUGHT A NEW COMPUTER

If you have just purchased a new computer and it is producing memory errors, the problem could be related to anything, including a bad computer board. In this case, you need to troubleshoot the entire computer, including memory. Because the computer dealer will have configured memory and run system tests before shipping, they can best help.

YOU'VE JUST INSTALLED NEW MEMORY

If you have just installed new memory, the first possibility is that you installed incorrect parts. Double-check the part numbers. Confirm that you have configured and installed the memory correctly.

YOU'VE INSTALLED NEW SOFTWARE OR OPERATING SYSTEM

Newer software or operating systems tend to push memory harder than older operating systems. Sometimes memory that worked fine prior to a software installation begins producing errors once it runs memory-intensive software. New software also has bugs, and beta versions are notorious for producing memory errors. In these cases, your first step should be to ensure you have the latest BIOS and service patches for your software. Otherwise contact the memory vendor. A technical support representative may have experience with other software incidents and can walk you through more-detailed troubleshooting.

YOU'VE INSTALLED OR REMOVED HARDWARE

If you have just installed or removed hardware and suddenly receive memory error messages, the first place to look is in the computer itself. A connection may have come loose during the installation or the new hardware may be defective; in either case the errors are manifesting themselves as memory problems. Make sure you have the latest drivers and firmware. Most hardware manufacturers will post updates on their Web sites.

UNEXPECTED PROBLEMS

If your system has been running fine, but suddenly starts to produce memory errors, and crash or lock up frequently, the chance of a hardware failure is more likely, since configuration and installation problems show up as soon as the computer turns on. Sometimes you can get memory problems if your computer is overheating, if you are having a problem with your power supply, or if corrosion has developed between the memory module and the socket, weakening the connection.

8.4. HANDLING SPECIFIC PROBLEMS

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8.4. HANDLING SPECIFIC PROBLEMS
Here is a list of the most common ways the computer informs you of a memory problem.

The computer won't boot, merely beeps.

The computer boots but the screen is blank.

The computer boots but the screen is blank.

The computer reports a memory error.
Memory mismatch error
Memory parity interrupt at xxxxx
Memory address error at xxxxx
Memory failure at xxxxx, read xxxxx, expecting xxxxx
Memory verify error at xxxxx

The computer has other problems caused by memory.
The computer intermittently reports errors, crashes frequently, or spontaneously reboots.
Registry Errors
General-protection faults, page faults, and exception errors

The server system manager reports a memory error.

The following translations help you understand what the computer means when it gives you one of these signals.

Computer won't boot, merely beeps.
Every time the computer starts, it takes inventory of hardware. Inventory consists of the computer BIOS recognizing, acknowledging, and in some cases, assigning addresses to, the components in the computer. If the computer won't boot, the CPU is unable to communicate with hardware. The cause can be improper installation or failure of the BIOS to recognize hardware. Follow basic troubleshooting, paying special attention to whether the memory module is completely installed and that you have the latest version of the BIOS.

Computer boots but doesn't recognize all the installed memory.When the computer boots, a part of the process is counting memory. On some machines the count appears on the screen and on others is masked. If the count is masked, from the computer set-up menu see how much memory the computer thinks it has. If the computer counts to or lists a number less than the memory you installed, the computer hasn't recognized all the memory.

Sometimes the computer will recognize only part of a module. This is almost always due to using the wrong kind of memory. For example, if your computer accepts only single-banked memory and you have installed dual-banked, the computer will read only half the memory on the module. Sometimes the computer will accept only modules containing memory chips with specific organizations. For example, the VX chipset doesn't work well with 64 Mbit chips.

In many computers the maximum amount of memory the computer can recognize is lower than the maximum amount you can physically install. For example, your computer may have three sockets, each of which can hold a 128MB module. If you filled every socket with 128MB, you would have 384MB of memory. However, your computer may recognize a maximum of 256MB. In most cases you can avoid this problem by consulting your computer manual or a memory configuration Web site before purchasing memory. Or visit the Kingston Web site.

The computer boots but the screen is blank.The most common reason for a blank screen is a dislodged card, memory not fully seated, or memory the computer doesn't support. Confirm that the memory is installed properly and that other components in the computer were not accidentally disconnected or dislodged while you installed memory.

Double-check that you have the right part number for the computer. If you have nonparity memory in a computer that requires error-checking memory, or SDRAM memory in a computer that supports only EDO, the screen may be blank at boot up.

The computer reports a memory error.
Memory mismatch error: This is not actually an error. Some computers require you to tell them that it's OK to have a new amount of memory. Use the set-up menu to tell the computer. Follow the prompts, enter the new amount, select Save, and exit.

Computer memory or address errors: All of the following errors, and those similar to them, indicate that the computer has a problem with memory:

Memory parity interrupt at xxxxx
Memory address error at xxxxx
Memory failure at xxxxx, read xxxxx, expecting xxxxx
Memory verification error at xxxxx

Typically the computer will perform a simple memory test as it boots. The computer will write information to memory and read it back. If the computer doesn't get what it was expecting, then it will report an error and sometimes give the address where the error occurred.

Such errors normally indicate a problem with a memory module but can sometimes indicate a defective motherboard or incompatibility between old and new memory. To verify that the new memory is causing the problem, remove the new memory and see whether the problem goes away. Then remove the old memory and install only the new memory. If the error persists, phone the memory manufacturer and ask for a replacement.

The computer has other problems caused by memory.
The Computer Intermittently Reports Errors, Crashes Frequently, or Spontaneously Reboots: Because of the large number of causes, these problems are difficult to diagnose. Possible causes are ESD (Electro-static Discharge), overheating, corrosion, or a faulty power supply. If you suspect ESD damage, contact the memory manufacturer and ask for a replacement. Before you install new memory, see page 85 for information on how to prevent ESD. If you suspect corrosion, clean the memory contacts and the sockets as explained on page 96. If you suspect the power supply, you will have to do overall computer troubleshooting with a focus on the power supply.

Registry Errors: Windows writes a large portion of the registry to RAM. Sometimes defective memory will cause registry errors. Windows reports a registry error and prompts you to restart and restore. If the prompts repeat, remove your newly installed memory and restart the computer. If the errors disappear, ask the memory manufacturer for replacement modules.

General-Protection Faults, Page Faults, and Exception Errors: The most common cause is software. For example, one application may not have released the memory after quitting or occupies the same memory addresses as another. In these cases, rebooting should solve the problem. If the computer suddenly displays general-protection faults, exception errors, or page faults after you have installed new memory, remove the new memory and see whether the errors stop. If they occur only when the new memory is installed, contact the memory manufacturer for assistance.

The server system manager reports a memory error.Most servers ship with system managers that monitor component utilization and test for abnormalities. Some of these system managers count soft errors in memory. Soft errors have been corrected by ECC memory. If the rate of soft errors is higher than specifications, however, the system manager issues a pre-failure warning. This warning enables the network administrator to replace the memory and prevent system downtime.

If the system manager on your server issues a pre-failure warning or other memory error, ask your memory manufacturer for a replacement. If the system manager continues to issue errors after memory replacement, make sure you have the latest BIOS, software service patches, and firmware. The chance of receiving two bad memory modules in a row is low. Contact the memory manufacturer for compatibility troubleshooting. Sometimes the server does not work well with certain types of memory chips or certain memory designs.

8.5. STILL NEED HELP?

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8.5. STILL NEED HELP?
Most memory manufacturers have FAQ or Q-and-A sections on their Web sites. There are also troubleshooting areas on the Web site of the computer manufacturer. If you can't find anything online, phone technical support for the computer or memory manufacturer. The next section gives information about Kingston and how to reach us.
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9. MORE ABOUT KINGSTON

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9. MORE ABOUT KINGSTON
9.1. COMPANY OVERVIEW
9.2. HOW TO REACH KINGSTON
9.3. WHY KINGSTON?
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9.1. COMPANY OVERVIEW

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9.1. COMPANY OVERVIEW
Founded in 1987, Kingston Technology is the world's largest independent manu-facturer of memory products. At the close of 1998, Kingston had sales in excess of $1.5 billion. Worldwide, the company presently staffs four manufacturing sites on four continents and six international sales and marketing facilities.

Kingston manufactures memory products that consistently meet or exceed the industry's stringent standards, possessing both the skill and equipment necessary to create the best modules in the marketplace.

The personal philosophy of company founders John Tu and David Sun, has been permanently imprinted into the corporate culture. From the company founders to the employees and ultimately, to the consumer, a special "magic" is infused into every product. At Kingston, it is the people that make the difference.

The Kingston spirit reflects an individual commitment...

CORE VALUES

Respect for one another in our culturally diverse environment

Loyalty to our long-term partnerships

Flexibility and adaptability in responding to our customers' needs

Investing in our employees to continuously improve our most valuable resource

Having fun working in the company of friends

9.2. HOW TO REACH KINGSTON

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9.2. HOW TO REACH KINGSTON
HOW TO REACH KINGSTON

U.S. HEADQUARTERS

Kingston Technology Company Toll Free: +1 (877) KINGSTON
17600 Newhope Street Tel: +1 (714) 435-2600
Fountain Valley, CA 92708 Fax: +1 (714) 435-2699
USA Internet: www.kingston.com

MEMORY-U.S.
PHONE/FAX NUMBER EMAIL ADDRESS
Memory Sales +1(877)KINGSTON
+1(714)435-2699 [email protected]
High-end Memory
Sales +1(888)435-5446
+1(714)435-2618 [email protected]
ValueRam Sales +1(877)435-8726
+1(714)445-3496 [email protected]
Flash Memory Sales +1(888)822-6315
+1(714)438-1879 [email protected]
Technical Support +1(800)435-0640
+1(714)424-3939 [email protected]
RMA +1(800)337-3719
+1(714)435-2643 [email protected]
MEMORY-INTL.
(Supporting All
Regions Except
Europe) PHONE/FAX NUMBER EMAIL ADDRESS
Memory Sales
(in English) +1(714)437-3334
+1(714)438-1820 [email protected]
Technical Support
(in English) +1(800)435-0640
+1(714)424-3939 [email protected]
Technical Support
(in Spanish) +1(888)822-6316
+1(714)424-3939 [email protected]
RMA (in Spanish) +1(714)437-3334
+1(714)438-1820 [email protected]
STORCASE TECHNOLOGY, INC. PHONE/FAX NUMBER EMAIL ADDRESS
StorCase Sales +1(800)435-0642
+1(714)438-1847 [email protected]
StorCase Technical
Support +1(714)438-1858
+1(714)438-1847 [email protected]

EUROPEAN HEADQUARTERS

Kingston Technology Europe, Inc. Tel: +44 (0) 1932 738 888
Kingston Court Fax: +44 (0) 1932 738 880
Sunbury-on-Thames
Middlesex TW16 7EP
England

EUROPEAN BRANCH OFFICES

Kingston Technology GmbH
Hoferstrasse 1
81737 Munich
Tel: +49 89 627 1560
Telefax: +49 49 89 627 15660

Kingston Technology France
171A, Avenue Charles De Gaulle
Tel: +33 1 46 43 9530
Tel: 0800 90 57 01 (Toll-free Customer Service within France)
Telefax: +33 1 46 43 9535
Telecopie: 0800 90 09 10 (Toll-free within France)

9.3. WHY KINGSTON?

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9.3. WHY KINGSTON?
ISO 9001 CERTIFICATION

Kingston is ISO 9001 certified as part of a continuing global effort to assure customers the highest quality service and products.

EXCEPTIONAL QUALITY

In addition to our ISO 9001 certification, we have established an extensive DCAT (Design, Components, Assembly, and Test) quality-control process to ensure total product reliability.

PROVEN INDUSTRY LEADER

Kingston has been making memory modules since 1987.

100% PRODUCT TESTING

Kingston tests every memory module before shipping. Our customized test equipment is so comprehensive that it can test every cell on every chip on every module-on a 64MB module, that's 512 million cells!

PREMIUM COMPONENTS

Kingston buys 100% of its memory chips from top-tier DRAM suppliers.

FREE TECHNICAL SUPPORT

Technical support professionals are available to answer your call 24 hours a day, 7 days a week at (800) 435-0640. Average wait time is less than 1 minute.

KINGSTON'S LIFETIME WARRANTY

With a lifetime warranty on all Kingston memory upgrades, network adapters, and processor upgrades, you have the most comprehensive warranty in the industry.

FREE EVALUATION UNITS

Kingston offers a free 30-day product evaluation program to qualified corporate customers.

100% COMPATIBILITY GUARANTEE

Kingston guarantees all memory products to be compatible with the system or family of systems for which they're designed.

OVERNIGHT PRODUCT REPLACEMENT

In the unlikely event your Kingston product needs repair or replacement, we will cross-ship a replacement product to you overnight (in most cases).

FREE LITERATURE

Kingston is committed to educating customers on memory and related technology. White papers, memory bits, and other informative tools are available free of charge in electronic and printed formats. Send requests to [email protected].

CORPORATE ALLIANCE PROGRAM (CAP)

As an extension of Kingston's service commitment, we offer Corporate Alliance membership to qualified IT professionals. Benefits include a dedicated Kingston representative, use of the Partner Purchase Program, on site tech support training, and special pricing.

FIELD SUPPORT

Kingston's field sales team is available for regional and on-site customer support. To find a representative in your area, go to www.kingston.com/contact/field.asp.

USER-FRIENDLY WEB SITE

Kingston's Web site www.kingston.com has the latest information on industry trends, promotions, product releases, and more.

A Basic Tutorial on Sampling Theory

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A Basic Tutorial on Sampling Theory
A basic tutorial on sampling theory is presented. Aliasing due to sampling of continuous-time signals is characterized mathematically.Shannon's sampling theorem is proved. A pictorial representation of continuous-time signal reconstruction from discrete-time samples is given.

A First Look at Taylor Series

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A First Look at Taylor Series
Any ''smooth'' function can be expanded in the form of a Taylor series:

About this document

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About this document ...
This document is a new HTML formatted version published by permission of:

"Music 320 Background Reader" by Julius O. Smith III, (Course Background Reader, Music 320). Copyright © 2001-01-02 by Julius O. Smith III. - Center for Computer Research in Music and Acoustics (CCRMA), Department of Electrical Engineering, Stanford University.

Acknowledgement

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Acknowledgement
Thanks to Craig Stuart Sapp ([email protected]">[email protected]) for contributing Figures8.2,8.3,8.4,8.6,8.7,8.8,8.9, and8.10.
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Alias Operator

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Alias Operator
Aliasing occurs when a signal is undersampled. If the signalsampling rate is too low, we get frequency-domain aliasing.

Aliasing of Sampled Continuous-Time Signals

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Aliasing of Sampled Continuous-Time Signals
This section quantifies aliasing in the general case. This result is then used in the proof of Shannon's Sampling Theorem in the next section.

An Example of Changing Coordinates in 2D

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An Example of Changing Coordinates in 2D
As a simple example, let's pick the following pair of new coordinate vectors in 2D

An Example Vector View

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An Example Vector View:
Consider the example two-sample signal graphed in Fig. 6.1.

An Orthonormal Sinusoidal Set

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An Orthonormal Sinusoidal Set
We can normalize the DFT sinusoids to obtain an orthonormal set:

Appendix A: Linear Time-Invariant Filters and Convolution

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Appendix A: Linear Time-Invariant Filters and Convolution
A reason for the importance of convolution is that every linear time-invariant system^8.9 can be represented by a convolution. Thus, in the convolution equation

Appendix A: Round-Off Error Variance

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Appendix A: Round-Off Error Variance
This section shows how to derive that the noise power of quantization error is , where is the quantization step size.

Appendix B: Electrical Engineering 101

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Appendix B: Electrical Engineering 101
The state of an ideal resistor is completely specified by the voltage across it (call it volts) and the current passing through it ( Amperes, or simply ''amps''). The ratio of voltage to current gives the value of the resistor ( resistance in Ohms). The fundamental relation between voltage and current in a resistor is calledOhm's Law:

Appendix B: Introductory Statistical Signal Processing

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Appendix B: Introductory Statistical Signal Processing
The correlation operator defined above plays a major role in statistical signal processing. This section gives a short introduction to some of the most commonly used elements. The student interested in mastering the concepts introduced briefly below may consider taking EE 278 in the Electrical Engineering Department. For further reading, see [16,20].

Appendix C: Mathematica/Matlab Examples

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Appendix C: Mathematica/Matlab Examples
Below is the Mathematica code for creating the aliasing example in Fig. 8.9.
aliasShow[freq_, srate_, options___] := SeqPlot[Sin[2 \[Pi] freq t / srate], {t, 0, srate-1},options, Continuous->True]
a = aliasShow[1, 10]; b = aliasShow[-9, 10, PlotStyle->RGBColor[1,0,0]]; Show[a, b, AspectRatio->1/3];

Appendix D: The Similarity Theorem

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Appendix D: The Similarity Theorem
The similarity theorem is fundamentally restricted to the continuous-time case. It says that if you ''stretch'' a signal by the factor in the time domain, you ''squeeze'' its Fourier transform by the same factor in the frequencydomain. This is such a fundamental Fourier relationship, that we include it here rather than leave it out as a non-DFT result.

Appendix: Matlab Examples

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Appendix: Matlab Examples
Here's how Fig. 6.1 was generated in Matlab:
>> x = [2 3]; % coordinates of x >> origin = [0 0]; % coordinates of the origin >> xcoords = [origin(1) x(1)]; % plot() expects coordinate lists, not endpoints >> ycoords = [origin(2) x(2)]; >> plot(xcoords,ycoords); % Draw a line from origin to x
Mathematica can plot a list of ordered pairs:
In[1]: ListPlot[{{0,0},{2,3}},PlotJoined->True]; (* Draw a line from (0,0) to (2,3) *)

Application of the Shift Theorem to FFT Windows

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Application of the Shift Theorem to FFT Windows
In practical spectrum analysis, we most often use the fast Fourier transform^8.6(FFT) together with a window function . Windows are normally positive (), symmetric about their midpoint, and look pretty much like a ''bell curve.'' A window multiplies the signal being analyzed to form a windowed signal , or , which is then analyzed using the FFT. The window serves to taper the data segment gracefully to zero, thus eliminating spectral distortions due to suddenly cutting off the signal in time. Windowing is thus appropriate when is a short section of a longer signal.

Applications of Cross-Correlation

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Applications of Cross-Correlation
The cross-correlation function is used extensively in pattern recognition and signal detection. We know that projecting one signal onto another is a means of measuring how much of the second signal is present in the first. This can be used to ''detect'' the presence of known signals as components of more complicated signals. As a simple example, suppose we record which we think consists of a signal which we are looking for plus some additive measurement noise. Then the projection of onto is

Audio Decay Time

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Audio Decay Time ()
In audio, a decay by is too small to be considered a practical ''decay time.'' In architectural acoustics (which includes the design of concert halls), a more commonly used measure of decay is '''', which is defined as the time to decay by dB.^5.5 That is, is obtained by solving the equation

Autocorrelation

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Autocorrelation
The cross-correlation of a signal with itself gives the autocorrelation function

Back to e

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Back to e
Above, we defined as the particular real number satisfying

Back to e^(j theta)

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Back to e^(j theta)
We've now defined for any positive real number and any complex number . Setting and gives us the special case we need for Euler's identity. Since is its own derivative, the Taylor series expansion for for is the simplest series there could be:

Bandlimited Interpolation in Time

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Bandlimited Interpolation in Time
The dual of the Zero-Padding Theorem states formally that zero padding in the frequency domain corresponds to ideal bandlimited interpolation in the time domain. However, we have not precisely defined ideal bandlimited interpolation in the time domain. Therefore, we'll let the dual of the Zero-Padding Theorem provide its definition:

Bibliography

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Bibliography
1
J. O. Smith,
''Introduction to digital filter theory'',
in Digital Audio Signal Processing: An Anthology, J. Strawn, Ed. William Kaufmann, Inc., Los Altos, California, 1985,
a shortened version appears in [23]. Also available as Stanford University Department of Music Technical Report STAN-M-20, April 1985.

Binary Integer Fixed-Point Numbers

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Binary Integer Fixed-Point Numbers
Most prevalent computer languages only offer two kinds of numbers,floating-point and integer fixed-point. On present-day computers, all numbers are encoded using binary digits (called ''bits'') which are either 1 or 0.^4.7 In C, C++, and Java, floating-point variables are declared as float (32 bits) or double (64 bits), while integer fixed-point variables are declared as short int(typically 16 bits and never less), long int (typically 32 bits and never less), or simply int (typically the same as a long int, but sometimes between short and long). For an 8-bit integer, one can use the char datatype (8 bits).

Cauchy-Schwarz Inequality

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Cauchy-Schwarz Inequality
The Cauchy-Schwarz Inequality (or ''Schwarz Inequality'') states that for all and , we have

Causal FIR Filters

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Causal FIR Filters
From Eq. (B.2), we that the impulse response is alwayszero for . Any filter having a zero impulse response prior to time is said to be causal. Thus, a tapped delay line such as that depicted in Fig. B.1 can only implement causal FIR filters. In software, however, we may easily implement non-causal filters as well based simply on the definition ofconvolution. However, noncausal filters are never precisely physical, of course, since events are causal in the real world (disregarding certain effects in quantum mechanics).

Changing the Base

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Changing the Base
By definition, . Taking the log base of both sides gives

Circular Motion

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Circular Motion
Since the modulus of the complex sinusoid is constant, it must lie on acircle in the complex plane. For example,

Coherence

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Coherence
A function related to cross-correlation is the coherence function, defined in terms of power spectral densities and the cross-spectral density by

Comparing Analog and Digital Complex Planes

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Comparing Analog and Digital Complex Planes
In signal processing, it is customary to use as the Laplace transform variable for continuous-time analysis, and as the -transform variable for discrete-time analysis. In other words, for continuous-time systems, the frequency domain is the '' plane'', while for discrete-time systems, the frequency domain is the '' plane.'' However, both are simply complex planes.

Complex Numbers

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Complex Numbers
This section introduces various notation and terms associated with complex numbers. As discussed above, complex numbers are devised by introducing the square-root of as a primitive new algebraic object among real numbers and manipulating it symbolically as if it were a real number itself:

Complex Roots

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Complex Roots

Figure 2.1:An example parabola defined by .

Complex Sinusoids

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Complex Sinusoids
Recall Euler's Identity,

Conclusions

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Conclusions
For the student interested in pursuing further the topics of this reader, see [18,19].

Conjugation and Reversal

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Conjugation and Reversal

Theorem: For any ,

Constructive and Destructive Interference of Sinusoids

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Constructive and Destructive Interference of Sinusoids
Sinusoidal signals are analogous to monochromatic laser light. You might have seen ''speckle'' associated with laser light, caused by destructive inteference of multiple reflections of the light beam. In a room, the same thing happens with sinusoidal sound. For example, play a simple sinusoidal tone (e.g., ''A-440'' which is a sinusoid at frequency Hz) and walk around the room with one ear plugged. If the room is reverberant you should be able find places where the sound goes completely away due to destructive interference. In between such places (which we call ''nodes'' in the soundfield), there are ''antinodes'' at which the sound is louder by 6 dB (amplitude doubled) due to constructive interference. In a diffuse reverberant soundfield, the distance between nodes is on the order of a wavelength (the ''correlation distance'' within the random soundfield).

Convolution

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Convolution

Definition: The convolution of two signals and in is denoted '''' and defined by

Convolution Representation

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Convolution Representation
Note that the output of the th delay element in Fig. B.1 is, , where is the input signalamplitude at time . The output signal is therefore
(B.1)
(B.2)
(B.3)
(B.4)

Convolution Representation of LTI Filters

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Convolution Representation of LTI Filters
If is the output of an LTI filter with input and impulse response , then is the convolution of with ,

Convolution Theorem

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Convolution Theorem

Theorem: For any ,

Correlation

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Correlation

Definition: The correlation operator for two signals and in is defined as

Correlation Theorem

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Correlation Theorem

Theorem: For all ,

Cross-Correlation

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Cross-Correlation

Definition: The circular cross-correlation of two signals and in may be defined by

DB for Display

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DB for Display
In practical signal processing, it is common to choose the maximum signal magnitude as the reference amplitude. That is, we normalize the signal so that the maximum amplitude is defined as 1, or 0 dB. This convention is also used by ''sound level meters'' in audio recording. When displaying magnitude spectra, the highest spectral peak is often normalized to 0 dB. We can then easily read off lower peaks as so many dB below the highest peak.

DB SPL

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DB SPL
Sound Pressure Level (SPL ) is defined using a reference which is approximately the intensity of 1000 Hz sinusoid that is just barely audible (0 ''phons''). In pressure units:

DBm Scale

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DBm Scale
One common dB scale in audio recording is the dBm scale in which the reference power is taken to be a milliwatt (1 mW) dissipated by a 600Ohm resistor. (See Appendix B for a primer on resistors, voltage, current, and power.)

DBV Scale

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DBV Scale
Another dB scale is the dBV scale which sets 0 dBV to 1 volt. Thus, a 100-volt signal is

De Moivre's Theorem

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De Moivre's Theorem
As a more complicated example of the value of the polar form, we'll proveDe Moivre's theorem:

Decibels

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Decibels
A decibel (abbreviated dB) is defined as one tenth of abel. The bel^4.2 is an amplitude unit defined for sound as the log (base 10) of the intensityrelative to some reference intensity,^4.3 i.e.,

Decimation Operator

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Decimation Operator

Definition: Decimation by is defined as taking every th sample, starting with sample :

Decimation Theorem (Aliasing Theorem)

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Decimation Theorem (Aliasing Theorem)

Theorem: For all ,

Derivation of Taylor Series Expansion with Remainder

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Derivation of Taylor Series Expansion with Remainder
We repeat the derivation of the preceding section, but this time we treat the error term more carefully.

Derivatives of f(x)=a^x

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Derivatives of f(x)=a^x
Let's apply the definition of differentiation and see what happens:

Device Servers: Network-Enabling Nearly Any Device

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Terminal and Print Servers -- Traditional Applications

Despite many of the advancements of the computer industry, there still exist a great many applications where serial I/O devices are the best or only solution. Terminal/print/serial servers have long been the best method for networking simple terminals, bar code readers, scanners or printers. Input devices attached to a serial port on a server can reach any host supporting the same protocols as that server. Printers can be shared over the network in the same manner, with a job from one protocol following a job from another. In the case of the print server that has multiple ports, jobs coming from hosts supporting different protocols can even print simultaneously.

DFT Math Outline

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DFT Math Outline
In summary, understanding the DFT takes us through the following topics:
Complex numbers
Complex exponents
Why ?
Euler's formula
Projecting signals onto signals via the inner product
The DFT as the coefficient of projection of a signal onto sinusoids
The IDFT as a weighted sum of the projections
Various Fourier theorems
Elementary time-frequency pairs
Practical spectrum analysis in Matlab

Difference Equation

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Difference Equation
Definition. The difference equation for a general, causal, linear time-invariant (LTI)digital filter is given by
(B.7)
(B.8)

Digital Filter Theory Summary

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Digital Filter Theory Summary
This section summarizes digital filter theory in a rather terse fashion suitable for review study. linearity,time-invariance and four basic representations of digital filters are defined: the difference equation coefficients,impulse response, transfer function, and frequency response. Next the concepts of phase delay and group delay are defined. This material is a subset of that in [1].

Does it Work?

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Does it Work?
It is straightforward to show that the ''additive synthesis'' reconstruction method of the previous section actually works exactly (in the periodic case) in the following sense:
The reconstructed signal is band-limited to , i.e., its Fourier transform is zero for all . (This is not quite true in the truncated case.)
The reconstructed signal passes through the samples exactly. (This is true in both cases.)

Dual of the Convolution Theorem

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Dual of the Convolution Theorem
The Dual^8.7 of the Convolution Theorem says thatmultiplication in the time domain is convolution in thefrequency domain:

Dynamic Range

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Dynamic Range
The dynamic range of a signal processing system can be defined as the maximum dB level sustainable without overflow (or other distortion) minus the dB level of the ''noise floor''.

Elementary Relationships

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Elementary Relationships
From the above definitions, one can quickly verify

Ethernet Tutorial Part I: Networking Basics

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As companies rely on applications like electronic mail and database management for core business operations, computer networking becomes increasingly more important. This tutorial helps to explain Ethernet and Fast Ethernet, which are two of the most popular technologies used in networking.

LANs (Local Area Networks)

A network is any collection of independent computers that communicate with one another over a shared network medium. LANs are networks usually confined to a geographic area, such as a single building or a college campus. LANs can be small, linking as few as three computers, but often link hundreds of computers used by thousands of people. The development of standard networking protocols and media has resulted in worldwide proliferation of LANs throughout business and educational organizations.

Ethernet Tutorial Part II: Adding Speed

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While repeaters allow LANs to extend beyond normal distance limitations, they still limit the number of nodes that can be supported. Bridges and switches, however, allow LANs to grow significantly larger by virtue of their ability to support full Ethernet segments on each port. Additionally, bridges and switches selectively filter network traffic to only those packets needed on each segment - this significantly increases throughput on each segment and on the overall network. By providing better performance and more flexibility for network topologies, bridges and switches will continue to gain popularity among network managers.

Ethernet Tutorial Part III: Sharing Devices

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Device Servers

A device server is defined as a specialized, network-based hardware device designed to perform a single or specialized set of server functions. It is characterized by a minimal operating architecture that requires no per seat network operating system license, and client access that is independent of any operating system or proprietary protocol. In addition the device server is a “closed box,” delivering extreme ease of installation, minimal maintenance, and can be managed by the client remotely via a Web browser.

Euler's Formula

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Euler's Formula
Since is the algebraic expression of in terms of its rectangular coordinates, the corresponding expression in terms of its polar coordinates is

Euler's Theorem

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Euler's Theorem
Euler's Theorem (or ''identity'' or ''formula'') is

Even and Odd Functions

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Even and Odd Functions
Some of the Fourier theorems can be succinctly expressed in terms of even and odd symmetries.

Example 1: FFT of a Simple Sinusoid

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Example 1: FFT of a Simple Sinusoid
Our first example is an FFT of the simple sinusoid

Example 2: FFT of a Not-So-Simple Sinusoid

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Example 2: FFT of a Not-So-Simple Sinusoid
Now let's increase the frequency in the above example by one-half of a bin:
% Example 2: Same as Example 1 but with a frequency between bins
f = 0.25 + 0.5/N; % Move the frequency off of the bin center by half a bin

Example 3: FFT of a Zero-Padded Sinusoid

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Example 3: FFT of a Zero-Padded Sinusoid
Interestingly, looking back at Fig. 9.2c, we see there are no negative dB values. Could this be right? To really see the spectrum, let's use some zero padding in the time domain to yield ideal interpolation in the freqency domain:

Example 4: Blackman Window

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Example 4: Blackman Window
Finally, to finish off this sinusoid, let's look at the effect of using aBlackman window (which has nice but suboptimal parameters for audio work). Figure 9.5a shows the Blackman window, Fig. 9.5b shows its magnitude spectrum on a dB scale, and Fig. 9.5c introduces the use of a more natural frequency axis which interprets the upper half of the bin numbers as negative frequencies. Here is the Matlab for it:
% Add a "Blackman window" % w = blackman(N); % if you have the signal processing toolbox w = .42-.5*cos(2*pi*(0:N-1)/(N-1))+.08*cos(4*pi*(0:N-1)/(N-1)); figure(5); subplot(3,1,1); plot(w,'*'); title('The Blackman Window'); xlabel('Time (samples)'); ylabel('Amplitude'); text(-8,1,'a)');
% Also show the window transform: xw = [w,zeros(1,(zpf-1)N)]; % zero-padded window (col vector) Xw = fft(xw); % Blackman window transform spec = 20log10(abs(Xw)); % Spectral magnitude in dB spec = spec - max(spec); % Usually we normalize to 0 db max spec = max(spec,-100*ones(1,nfft)); % clip to -100 dB subplot(3,1,2); plot(fni,spec,’-’); axis([0,1,-100,10]); grid; xlabel(‘Normalized Frequency (cycles per sample))’); ylabel(‘Magnitude (dB)’); text(-.12,20,‘b)’);

Example 5: Use of the Blackman Window

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Example 5: Use of the Blackman Window
Now let's apply this window to the sinusoidal data:
% Use the Blackman window on the sinusoid data xw = [w .* cos(2*pi*n*f*T),zeros(1,(zpf-1)*N)]; % windowed, zero-padded data X = fft(xw); % Smoothed, interpolated spectrum
% Plot time data figure(6); subplot(2,1,1); plot(xw);
title(‘Windowed, Zero-Padded, Sampled Sinusoid’); xlabel(‘Time (samples)’); ylabel(’Amplitude’); text(-50,1,‘a)’); hold off;

Example 6: Hanning-Windowed Complex Sinusoid

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Example 6: Hanning-Windowed Complex Sinusoid
In this example, we'll perform spectrum analysis on a complex sinusoidhaving only a single positive frequency. We'll use the Hanning window which does not have as much sidelobe suppression as the Blackman window, but its main lobe is narrower. Its sidelobes ''roll off'' very quickly versus frequency. Compare with the Blackman window results to see if you can see these differences.
% Example 5: Practical spectrum analysis of a sinusoidal signal
% Analysis parameters: M = 31; % Window length (we’ll use a “Hanning window”) N = 64; % FFT length (zero padding around a factor of 2)

Example Applications of the DFT

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Example Applications of the DFT
This chapter goes through some practical examples of FFT analysis inMatlab. The various Fourier theorems provide a ''thinking vocabulary'' for understanding elements of spectral analysis.

Example Sinusoids

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Example Sinusoids
Figure 5.1 plots the sinusoid , for , , , and. Study the plot to make sure you understand the effect of changing each parameter (amplitude, frequency, phase), and also note the definitions of ''peak-to-peak amplitude'' and ''zero crossings.''

Exponentials

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Exponentials
The canonical form of an exponential function, as typically used in signal processing, is

Factoring a Polynomial with Real Roots

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Factoring a Polynomial with Real Roots
Remember ''factoring polynomials''? Consider the second-order polynomial

Figure 7.2

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Figure 7.2
Below is the Matlab for Fig. 7.2:
N=8; fs=1;
n = [0:N-1]; % row t = [0:0.01:N]; % interpolated k=fliplr(n)’ - N/2; fk = kfs/N; wk = 2pifk; clf; for i=1:N subplot(N,2,2i-1); plot(t,cos(wk(i)t)) axis([0,8,-1,1]); hold on; plot(n,cos(wk(i)n),’’) if i==1 title(‘Real Part’); end; ylabel(sprintf(‘k=%d’,k(i))); if i==N xlabel(‘Time (samples)’); end; subplot(N,2,2i); plot(t,sin(wk(i)*t)) axis([0,8,-1,1]); hold on; plot(n,sin(wk(i)n),’’) ylabel(sprintf(‘k=%d’,k(i))); if i==1 title(‘Imaginary Part’); end; if i==N xlabel(‘Time (samples)’); end; end

Figure 7.3

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Figure 7.3
Below is the Matlab for Fig. 7.3:
% Parameters (sampling rate = 1) N = 16; % DFT length k = N/4; % bin where DFT filter is centered wk = 2*pi*k/N; % normalized radian center-frequency for DFT_k() wStep = 2*pi/N; w = [0:wStep:2*pi - wStep]; % DFT frequency grid
interp = 10; N2 = interpN; % Denser grid showing “arbitrary” frequencies w2Step = 2pi/N2; w2 = [0:w2Step:2pi - w2Step]; % Extra dense frequency grid X = (1 - exp(j(w2-wk)N)) ./ (1 - exp(j(w2-wk))); % slightly offset to avoid divide by zero at wk X(1+k*interp) = N; % Fix divide-by-zero point (overwrite “NaN”)

Figuring Out Sampling Theory by Playing Around with Complex Sinusoids

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Figuring Out Sampling Theory by Playing Around with Complex Sinusoids
Consider , with . Then we can write in polar form as

Finiteness

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Finiteness
From Eq. (B.4), we see that the maximum length of the impulse response is samples. Therefore, a tapped delay line can only implement impulse responses of finite length, i.e., FIR filters.

FIR Filters

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FIR Filters
FIXME: Consider adding a section here on the one-zero filter, as in the filter tutorial. Or scan it, finally.

Flip Operator

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Flip Operator

Definition: We define the flip operator by

Floating-Point Numbers

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Floating-Point Numbers
Floating-point numbers consist of an ''exponent,'' ''significand'', and ''sign bit''. For a negative number, we may set the sign bit of the floating-point word and negate the number to be encoded, leaving only nonnegative numbers to be considered. Zero is represented by all zeros, so now we need only consider positive numbers.

Footnotes

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... sample.^1.1
Note that the definition of has changed unless the sampling rate really is 1, and the definition of has changed no matter what the sampling rate is, since when , , not .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
... unknowns.^2.1
''Linear'' in this context means that the unknowns are multiplied only by constants--they may not be multiplied by each other or raised to any power other than (e.g., not squared or cubed or raised to the power). Linear systems of equations in unknowns are very easy to solve compared to nonlinear systems of equations in unknowns. For example, Matlab or Mathematica can easily handle them. You learn all about this in a course on Linear Algebra which is highly recommended for anyone interested in getting involved with signal processing. Linear algebra also teaches you all about matrices which we will only introduce briefly in this course.
To give you a simple first exposure, here's how the linear system of equations

Formal Statement of Taylor's Theorem

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Formal Statement of Taylor's Theorem
Let be continuous on a real interval containing (and ), and let exist at and be continuous for all . Then we have the following Taylor series expansion:

Fourier Theorems for the DFT

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Fourier Theorems for the DFT
This chapter derives various Fourier theorems for the case of the DFT. Included are symmetry relations, the shift theorem, convolution theorem,correlation theorem, power theorem, and theorems pertaining to interpolation and downsampling. Applications related to certain theorems are outlined, including linear time-invariant filtering, sampling rate conversion, andstatistical signal processing.

Fractional Binary Fixed-Point Numbers

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Fractional Binary Fixed-Point Numbers
In ''DSP chips'' (microprocessors explicitly designed for digital signal processing applications), the most commonly used fixed-point format isfractional fixed point, also in two's complement.

Frequencies in the \

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Frequencies in the ''Cracks''
The DFT is defined only for frequencies . If we are analyzing one or more periods of an exactly periodic signal, where the period is exactly samples (or some integer divisor of ), then these really are the only frequencies present in the signal, and the spectrum is actually zero everywhere but at . However, we use the DFT to analyze arbitrary signals from nature. What happens when afrequency is present in a signal that is not one of the DFT-sinusoid freqencies ?

Frequency Response

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Frequency Response
Beginning with Eq. (B.4.3), we have

Further Notes on Differentiability of Audio Signals

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Further Notes on Differentiability of Audio Signals
As mentioned earlier, every audio signal can be regarded as infinitely differentiable due to the finite bandwidth of human hearing. One of the Fourier properties we will learn later in this course is thata signal cannot be both time limited and frequency limited.Therefore, by conceptually ''lowpass filtering'' every audio signal to reject all frequencies above kHz, we implicitly make every audio signal last forever! Another way of saying this is that the ''ideal lowpass filter `rings' forever''. Such fine points do not concern us in practice, but they are important for fully understanding the underlying theory. Since, in reality, signals can be said to have a true beginning and end, we must admit in practice that all signals we work with have infinite-bandwidth at turn-on and turn-off transients.^3.1

General Conditions

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General Conditions
This section summarizes and extends the above derivations in a somewhat formal manner (following portions of chapter 4 of ).

General Formula for Two's-Complement, Integer Fixed-Point Numbers

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General Formula for Two's-Complement, Integer Fixed-Point Numbers
Let denote the (even) number of bits. Then the value of a two's complement integer fixed-point number can be expressed in terms of its bits as

Generalized Complex Sinusoids

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Generalized Complex Sinusoids
We have defined sinusoids and extended the definition to include complex sinusoids. We now extend one more step by allowing for exponential amplitude envelopes:

Geometric Series

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Geometric Series
Recall that for any compex number , the signal , , defines a geometric sequence, i.e., each term is obtained by multiplying the previous term by a (complex) constant. A geometric series is defined as the sum of a geometric sequence:

Geometric Signal Theory

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Geometric Signal Theory
This chapter provides an introduction to the elements of geometric signal theory, including vector spaces, norms, inner products,orthogonality, projection of one signal onto another, and elementary vector space operations.

Gram-Schmidt Orthogonalization

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Gram-Schmidt Orthogonalization

Theorem: Given a set of linearly independent vectors from , we can construct an orthonormalset which are linear combinations of the original set and which span the same space.

Graphical Convolution

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Graphical Convolution
Note that the cyclic convolution operation can be expressed in terms of previously defined operators as

Guide to Using Fast Ethernet

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The demand for higher transmission speeds for near-term network growth has been realized by the new Fast Ethernet specification (IEEE 802.3u) known as 100BASE-T. This new LAN standard has raised the Ethernet speed limit from 10 Megabits per second to 100 Megabits per second with only minimal changes to the existing cable structure. The building blocks of today’s networks call out for a mixture of legacy 10BASE-T Ethernet networks and Fast Ethernet.

How Many Bits are Enough for Digital Audio?

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How Many Bits are Enough for Digital Audio?
Armed with the above knowledge, we can visit the question ''how many bits are enough'' for digital audio. Since the threshold of hearing is around 0db SPL, the ''threshold of pain'' is around 120 dB SPL, and each bit in a linear PCM format is worth about 6 dB of dynamic range, we find that we need bits to represent the full dynamic range of audio in a linear fixed-point format. This is a simplestic analysis because it is not quite right to equate the least-significant bit with the threshold of hearing; instead, we would like to adjust the quantization noisefloor to just below the threshold of hearing. Since the threshold of hearing is non-uniform, we would also prefer a shaped quantization noise floor (a feat that can be accomplished using filtered error feedback^4.9 Nevertheless, the simplistic result gives an answer similar to the more careful analysis, and 20 bits is a good number. However, this still does not provide forheadroom needed in a digital recording scenario. We also need both headroom and guard bits on the lower end when we plan to carry out a lot of signal processing operations, especially digital filtering. As an example, a 1024-point FFT (Fast Fourier Transform) can give amplitudes 1024 times the input amplitude (such as in the case of a constant ''dc'' input signal), thus requiring 10 headroom bits. In general, 24 fixed-point bits are pretty reasonable to work with, although you still have to scale very carefully, and 32 bits are preferable.

Imaginary Exponents

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Imaginary Exponents
We may define imaginary exponents the same way that all sufficiently smooth real-valued functions of a real variable are generalized to the complex case--using Taylor series. A Taylor series expansion is just a polynomial (possibly of infinitely high order), and polynomials involve only addition, multiplication, and division. Since these elementary operations are also defined for complex numbers, any smooth function of a real variable may be generalized to a function of a complex variable by simply substituting the complex variable for the real variable in the Taylor series expansion.

In-Phase and Quadrature Sinusoidal Components

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In-Phase and Quadrature Sinusoidal Components
From the trig identity , we have

Index

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Index
20 dB boost
Properties of DB Scales
3 dB boost
Properties of DB Scales
convolution
Convolution Representation of LTI
Aliasing
Alias Operator
aliasing operator
Alias Operator
amplitude response
LTI Filters and the | Frequency Response | Frequency Response
anti-aliasing lowpass filter
Alias Operator
antilog
Logarithms
antilogarithm
Logarithms
antisymmetric functions
Even and Odd Functions
average power
Appendix A: Round-Off Error
base
Logarithms
base logarithm
Logarithms
base logarithm
Logarithms
bel
Decibels
bin number
Frequencies in the ''Cracks''
binary
Binary Integer Fixed-Point Numbers
binary digits
Binary Integer Fixed-Point Numbers
bits
Binary Integer Fixed-Point Numbers
canonical with respect to delay
Order
causal
Causal FIR Filters | Difference Equation
characteristic of the logarithm
Logarithms
coefficient of projection
The Discrete Fourier Transform
column-vector
Matrices
comb-filter
Constructive and Destructive Interference
common logarithm
Logarithms
commutativity of convolution
Convolution
companding
Dynamic Range
complex matrix
Matrices
complex matrix transpose
Matrices
convolution
Convolution
convolution operator ''''
Convolution Representation
convolution representation
Appendix A: Linear Time-Invariant
correlation operator
Correlation
cross-talk
Frequencies in the ''Cracks''
cyclic convolution
Convolution
dB scale
Decibels
decibel
Decibels
decimal numbers
Binary Integer Fixed-Point Numbers
DFT as a digital filter
Frequencies in the ''Cracks''
DFT matrix
The DFT Matrix
difference equation
Difference Equation
difference equation coefficients
Difference Equation
digit
Binary Integer Fixed-Point Numbers
digital filter
Appendix A: Linear Time-Invariant
Discrete Fourier Transform
The DFT and its
Discrete Fourier Transform (DFT)
The DFT
dynamic range
Dynamic Range
dynamic range of magnetic tape
Dynamic Range
energy
Decibels
Euler's Formula
Euler's Formula
Euler's Theorem
Euler's Theorem
even functions
Even and Odd Functions
expected value
Appendix A: Round-Off Error
fast convolution
Convolution Theorem
filter
Digital Filter Theory Summary
filter coefficients
Difference Equation
filter delay for amplitude envelopes
Phase Delay and Group
filter order
Difference Equation
filter power response
Frequency Response
filter time delay
Phase Delay and Group
finite-impulse-response filter
FIR Filters
FIR filter
FIR Filters
flip operator
Flip Operator
Fourier Dual
Dual of the Convolution
frequency bin
Frequencies in the ''Cracks''
frequency response
LTI Filters and the | Frequency Response
frequency-domain aliasing
Alias Operator | Alias Operator
geometric sequence
Geometric Series
geometric series
Geometric Series
group delay
Phase Delay and Group
Hermitian spectra
Symmetry
Hermitian symmetry
Conjugation and Reversal
Hermitian transpose
Matrices
hex
Binary Integer Fixed-Point Numbers
hexadecimal
Binary Integer Fixed-Point Numbers
ideal bandlimited interpolation
Zero Padding Theorem | Bandlimited Interpolation in Time
ideal lowpass filtering operation in the frequency domain
Bandlimited Interpolation in Time
identity matrix
Matrix Multiplication
IDFT
The DFT and its
impulse response
Appendix A: Linear Time-Invariant | FIR Filters | Difference Equation
impulse signal
Appendix A: Linear Time-Invariant | FIR Filters | Difference Equation
indicator function
Linear Phase Terms
Intensity
Decibels
intensity level
DB SPL
interpolation operator
Zero Padding Theorem
inverse DFT
The DFT | The DFT and its
inverse DFT matrix
The DFT Matrix
irrational number
Real Exponents
JND
Decibels
just-noticeable difference
Decibels
lag
Correlation
lagged product
Correlation
length even rectangular windowing operation
Bandlimited Interpolation in Time
linear
Linearity and Time-Invariance
linear filter
Linearity and Time-Invariance
linear phase FFT windows
Application of the Shift
linear phase signal
Linear Phase Terms
linear phase term
Shift Theorem | Linear Phase Terms
linear transformation
Matrix Multiplication
logarithm
Logarithms
loudness
DB SPL
LTI filters
Linearity and Time-Invariance
main lobe
Frequencies in the ''Cracks''
mantissa
Logarithms
matrix
Matrices
matrix columns
Matrices
matrix multiplication
Matrix Multiplication
matrix rows
Matrices
matrix transpose
Matrices
mean
Appendix A: Round-Off Error
mean of a random variable
Appendix A: Round-Off Error
mean of a signal
Appendix A: Round-Off Error
mean square
Appendix A: Round-Off Error
modulo
Modulo Indexing, Periodic Extension
moments
Appendix A: Round-Off Error
multiplication of large numbers
Logarithms
multiplying two numbers convolves their digits
Multiplication of Decimal Numbers
natural logarithm
Logarithms
non-commutativity of matrix multiplication
Matrix Multiplication
normalized inverse DFT matrix
The DFT Matrix
normalized DFT matrix
The DFT Matrix
normalized DFT sinusoids
An Orthonormal Sinusoidal Set | Normalized DFT
normalized frequency
The DFT and its
octal
Binary Integer Fixed-Point Numbers
odd functions
Even and Odd Functions
order
Order
orthogonal
The DFT Matrix
orthogonality of sinusoids
Orthogonality of Sinusoids
orthonormal
The DFT Matrix
PCM
Pulse Code Modulation (PCM)
periodic
Modulo Indexing, Periodic Extension
periodic extension
Frequencies in the ''Cracks'' | Modulo Indexing, Periodic Extension
phase delay
Phase Delay and Group
phase response
LTI Filters and the | Frequency Response | Frequency Response
phase response at zero frequency
Phase Delay and Group
phon amplitude scale
DB SPL
polar form
Rational Exponents
polynomial approximation
Derivation of Taylor Series
power
Decibels
pressure
Decibels
primitive th root of unity
Orthogonality of Sinusoids
rational
Rational Exponents
real filter
Difference Equation
rectangular window
Frequencies in the ''Cracks''
rms level
Appendix A: Round-Off Error
roots of unity
Orthogonality of Sinusoids
row-vector
Matrices
sample mean
Appendix A: Round-Off Error
sample variance
Appendix A: Round-Off Error
second central moment
Appendix A: Round-Off Error
sensation level
DB SPL
shift operator
Shift Operator
sidelobes
Frequencies in the ''Cracks''
signal
Digital Filter Theory Summary
signal dynamic range
Dynamic Range
similarity theorem
Appendix D: The Similarity
sinc function
Frequencies in the ''Cracks''
skew-Hermitian
Conjugation and Reversal
sone amplitude scale
DB SPL
Sound Pressure Level
DB SPL
spectral leakage
Frequencies in the ''Cracks''
spectrum
The Discrete Fourier Transform | The DFT and its
SPL
DB SPL
square matrix
Matrices
stable
Difference Equation
standard deviation
Appendix A: Round-Off Error
Stretch Operator
no title | Stretch Operator
symmetric functions
Even and Odd Functions
Taylor Series Expansion
no title | Informal Derivation of Taylor
time-domain aliasing
Alias Operator
time-invariant
Linearity and Time-Invariance
Toeplitz
Matrix Multiplication
transfer function
Transfer Function | Convolution Representation of LTI
transform pair
Notation and Terminology
transpose of a matrix product
Matrix Multiplication
unilateral transform
Convolution Representation of LTI
unit pulse signal
Appendix A: Linear Time-Invariant
unitary
The DFT Matrix
variance
Appendix A: Round-Off Error
window
Frequencies in the ''Cracks''
Zero padding
Zero Padding
zero phase signal
Symmetry

Informal Derivation of Taylor Series Expansion

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Informal Derivation of Taylor Series Expansion
We have a function and we want to approximate it using anth-order polynomial:

Introduction

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Introduction
Inside computers and modern ''digital'' synthesizers, (as well as music CDs), sound is sampled into a stream of numbers. Each sample can be thought of as a number which specifies the position of a loudspeaker at a particular instant. When sound is sampled, we call itdigital audio. The sampling rate used for CDs is 44,100 samples per second. That means when you play a CD, the speakers in your stereo system are moved to a new position 44,100 times per second, or once every 23 microseconds. Controlling a speaker this fast enables it to generate any sound in the human hearing range because we cannot hear frequencies higher than around 20,000 cycles per second, and a sampling rate more than twice the highest frequency in the sound guarantees that exact reconstruction is possible from the samples.

Introduction to Complex Numbers

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Introduction to Complex Numbers
This chapter provides an introduction to complex numbers, factoring polynomials, the quadratic formula, the complex plane, Euler's formula, and an overview of numerical facilities for complex numbersin Matlab and Mathematica.

Introduction to Digital Filter Analysis

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Introduction to Digital Filter Analysis
The subject of digital filtering is quite large, and many books are devoted entirely to that subject from different points of view. This chapter discusses only the filter structures we need, such as basicFIR filters and BiQuads. The last section summarizes the main point of digital filter theory.

Introduction to the DFT

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Introduction to the DFT
This chapter introduces the Discrete Fourier Transform (DFT) and points out the elements which will be discussed in the Music 320 Background Reader.

Law Companding

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-Law Companding
A companding operation compresses dynamic range on encode andexpands dynamic range on decode. In digital telephone networks and voice modems (currently in use everywhere), standard CODEC^4.14 chips are used in which audio is digitized in a simple 8-bit -law format (or simply ''mu-law'').

Linear Number Systems for Digital Audio

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Linear Number Systems for Digital Audio
This section discusses the most commonly used number formats for digital audio.

Linear Phase Terms

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Linear Phase Terms
The reason is called a linear phase term is that its phase is a linear function of frequency:

Linearity

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Linearity

Theorem: For any and , the DFT satisfies

Linearity and Time-Invariance

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Linearity and Time-Invariance
In everyday terms, the fact that a filter islinear means simply that
the amplitude of the output is proportional to the amplitude of the input, and

Linearity of the Inner Product

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Linearity of the Inner Product
Any function of a vector (which we may call an operator on ) is said to be linear if for all and , and for all scalars and in , we have

Little Endian Formula

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''Little Endian'' Formula for Two's-Complement, Integer Fixed-Point Numbers
The formula of the preceding section can be considered ''big endian'' because the bits are labeled ''left to right'' in the word as it is normally visualized. That is, is the most significant bit instead of the least significant bit. The ''little endian'' convention numbers bits in order of their significance instead.

Logarithmic Fixed-Point Numbers

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Logarithmic Fixed-Point Numbers
In some situations it makes sense to use logarithmic fixed-point. This number format can be regarded as a floating-point format consisting of an exponent and no explicit significand. However, the exponent is not interpreted as an integer as it is in floating point. Instead, it has a fractional part which is a true mantissa. (The integer part is then of course the ''characteristic'' of the logarithm.) In other words, a logarithmic fixed-point number is a binary encoding of the log-base-2 of the signal-sample magnitude. The sign bit is of course separate.

Logarithmic Number Systems for Digital Audio

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Logarithmic Number Systems for Digital Audio
Since hearing is approximately logarithmic, it makes sense to represent sound samples in a logarithmic or semi-logarithmic number format.Floating-point numbers in a computer are partially logarithmic (the exponent part), and one can even use an entirely logarithmic fixed-pointnumber system. The -law amplitude-encoding format is linear at small amplitudes and becomes logarithmic at large amplitudes. This section discusses these formats.

Logarithms

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Logarithms
A logarithm is fundamentally an exponent applied to a specific base . That is, . The term ''logarithm'' can be abbreviated as ''log''. The base is chosen to be a positive real number, and we normally only take logs of positive real numbers (although it is ok to say that the log of is ). The inverse of a logarithm is called anantilogarithm or antilog.

Logarithms of Negative and Imaginary Numbers

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Logarithms of Negative and Imaginary Numbers
By Euler's formula, , so that

Logarithms, Decibels, and Number Systems

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Logarithms, Decibels, and Number Systems
This chapter provides an introduction to logarithms (real and complex),decibels, and number systems such as binary integer fixed-point, fractional fixed-point, one's complement, two's complement, logarithmic fixed-point,-law, and floating-point number formats.

LTI Filters and the Convolution Theorem

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LTI Filters and the Convolution Theorem

Definition: The frequency response of an LTI filter is defined as the Fourier transform of its impulse response. In particular, for finite, discrete-time signals , the sampled frequency response is defined as

Mathematica for Selected Plots

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Mathematica for Selected Plots
The Mathematica code for producing Fig. 5.1 (minus the annotations which were done using NeXT Draw and EquationBuilder from Lighthouse Design) is
Plot[10 Sin[2 Pi 2.5 t + Pi/4],{t,0,1}, PlotLabel->"10 Sin[2 Pi 2.5 t + Pi/4]", PlotPoints->500, AxesLabel->{" Sec", "Amp."}];

Mathematics of the DFT

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Mathematics of the DFT
In the signal processing literature, it is common to write the DFT in the more pure form obtained by setting in the previous definition:

Matlab Examples

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Matlab Examples

Subsections
Figure 7.2
Figure 7.3
DFT Matrix

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Matrices

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Matrices
A matrix is defined as a rectangular array of numbers, e.g.,

Matrix Formulation of the DFT

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Matrix Formulation of the DFT
The DFT can be formulated as a complex matrix multiply.

Subsections
Matrices
Matrix Multiplication
The DFT Matrix

Matrix Multiplication

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Matrix Multiplication
Let be a general matrix and let denote a general matrix. Denote the matrix product by or . Then matrix multiplication is carried out by computing the inner product of every row of with every column of . Let theth row of be denoted by , , and theth column of by , . Then the matrix product is defined as

Method 1: Additive Synthesis

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Method 1: Additive Synthesis
One reasonable definition for can be based on the DFT of :

Modulo Indexing, Periodic Extension

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Modulo Indexing, Periodic Extension
The DFT sinusoids are all periodichaving periods which divide . That is, for any integer . Since a length signal can be expressed as a linear combination of the DFT sinusoids in the time domain,

More Notation and Terminology

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More Notation and Terminology
It's already been mentioned that the rectilinear coordinates of a complex number in the complex plane are called the real part andimaginary part, respectively.

Motivating Example and Overview

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Motivating Example and Overview
Suppose you look up the documentation for a ''comb filter'' in a software package you are using, and you find it described as follows:
out(n) = input(n) + feedforward * input(n-delay1) - feedback * out(n-delay2)
Does this tell you everything you need to know? Well, it does tell you exactly what is implemented, but to really understand it, you need to see its frequency response. Moreover, if delay2corresponds to more than a a few milliseconds, you probably want to see its impulse response as well. The purpose of this appendix is to describe how to do this analysis.

Multiplication of Decimal Numbers

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Multiplication of Decimal Numbers
Since decimal numbers are implicitly just polynomials in the powers of 10, e.g.,

Music 320 Background Reader Mathematics of the Discrete Fourier Transform (DFT)

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Music 320 Background Reader
Mathematics of the Discrete Fourier Transform (DFT)
Julius O. Smith III([email protected]">[email protected])
Center for Computer Research in Music
and Acoustics (CCRMA)
Department of Music,Stanford University
Stanford, California 94305

Negative Exponents

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Negative Exponents
What should be? Multiplying it by gives

Network Switching Tutorial

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Switches are great, they add network capacity and speed, but they are not a cure-all. How can you tell if your network will benefit from switching? And how do you add switches to your network design for the most benefit? This tutorial is written to answer these questions. Along the way we’ll describe how switches work, and how they both harm and benefit your networking strategy. And we¹ll discuss different network types, so you can profile your network and gauge the potential benefit of switching for your environment.

Norm Induced by the Inner Product

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Norm Induced by the Inner Product
We may define a norm on using the inner product:

Norm of the DFT Sinusoids

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Norm of the DFT Sinusoids
For , we follow the previous derivation to the next-to-last step to get

Normalized DFT

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Normalized DFT
A more ''theoretically clean'' DFT is obtained by projecting onto thenormalized DFT sinusoids

Notation and Terminology

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Notation and Terminology
If is the DFT of , we say that and form a transform pair and write

Numerical Tools in Mathematica

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Numerical Tools in Mathematica
In Mathematica, we can find the roots of simple polynomials in closed form, while larger polynomials can be factored numerically in eitherMatlab or Mathematica. Look to Mathematica to provide the most sophisticated symbolic mathematical manipulation, and look for Matlab to provide the best numerical algorithms, as a general rule.

Numerical Tools in Matlab

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Numerical Tools in Matlab
In Matlab, root-finding is always numerical:^2.3
>> % polynomial = array of coefficients in Matlab >> p = [1 0 0 0 5 7]; % p(x) = x^5 + 5*x + 7 >> format long; % print double-precision >> roots(p) % print out the roots of p(x)
ans = 1.30051917307206 + 1.10944723819596i 1.30051917307206 - 1.10944723819596i -0.75504792501755 + 1.27501061923774i -0.75504792501755 - 1.27501061923774i -1.09094249610903

One's Complement Fixed-Point Format

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One's Complement Fixed-Point Format
One's Complement is a particular assignment of bit patterns to numbers. For example, in the case of 3-bit binary numbers, we have the assignments shown in Table 4.3.

Order

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Order
The order of a filter is defined as the order of its transfer function. Thus, from Eq. (B.2), the order of a causal, length FIR filter is (provided ).

Orthogonality

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Orthogonality
The vectors (signals) and are said to be orthogonal if , denoted . That is to say

Orthogonality of Sinusoids

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Orthogonality of Sinusoids
A key property of sinusoids is that they are orthogonal at different frequencies. That is,

Orthogonality of the DFT Sinusoids

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Orthogonality of the DFT Sinusoids
We now show mathematically that the DFT sinusoids are exactly orthogonal. Let

Other Norms

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Other Norms
Since our main norm is the square root of a sum of squares, we are using what is called an norm and we may write to emphasize this fact.

Outline

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Outline
Below is an overview of the chapters.
Introduction to the DFT
This chapter introduces the Discrete Fourier Transform (DFT) and points out the elements which will be discussed in this reader.

Phase Delay and Group Delay

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Phase Delay and Group Delay
The phase response of a filter gives the radian phase shift experienced by each sinusoidal component of the input signal. Sometimes it is more meaningful to consider phase delay[21].

Polynomial Multiplication

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Polynomial Multiplication
Note that when you multiply two polynomials together, their coefficients are convolved. To see this, let denote the th-order polynomial

Positive and Negative Frequencies

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Positive and Negative Frequencies
Earlier, we used Euler's Identity to show

Positive Integer Exponents

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Positive Integer Exponents
The ''original'' definition of exponents which ''actually makes sense'' applies only to positive integer exponents:

Power Theorem

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Power Theorem

Theorem: For all ,

Powers of

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Powers of
Choose any two complex numbers and , and form the sequence

Preface

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Preface
This chapter is an outgrowth of my course entitled''Introduction to Digital Signal Processing and the Discrete Fourier Transform (DFT)which I have given at the Center for Computer Research in Music and Acoustics (CCRMA) every year for the past 16 years. The course was created primarily as a first course in digital signal processing for entering Music Ph.D. students. As a result, the only prerequisite is a good high-school math background. Calculus exposure is desirable, but not required.

Projection

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Projection
The orthogonal projection (or simply ''projection'') of onto is defined by

Projection of Circular Motion

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Projection of Circular Motion
We have

Proof of Euler's Identity

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Proof of Euler's Identity
This chapter outlines the proof of Euler's Identity, which is an important tool for working with complex numbers. It is one of the critical elements of the DFT definition that we need to understand.

Properties of DB Scales

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Properties of DB Scales
In every kind of dB, a factor of 10 in amplitude gain corresponds to a 20 dB boost (increase by 20 dB):

Properties of Exponents

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Properties of Exponents
From the basic definition of positive integer exponents, we have
(1)
(2)
Note that property (2) implies property (1). We list it explicitly for convenience below.

Pulse Code Modulation (PCM)

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Pulse Code Modulation (PCM)
The ''standard'' number format for sampled audio signals is officially called Pulse Code Modulation (PCM). This term simply means that each signal sample is interpreted as a ''pulse'' (e.g., a voltage or current pulse) at a particular amplitude which is binary encoded, typically in two's complement binary fixed-point format (discussed below). When someons says they are giving you a soundfile in ''raw binary format'', they pretty much always mean (nowadays) 16-bit, two's-complement PCM data. Most mainstream computer soundfile formats consist of a ''header'' (containing the length, etc.) followed by 16-bit two's-complement PCM.

Rational Exponents

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Rational Exponents
A rational number is a real number that can be expressed as a ratio of two integers:

Rayleigh Energy Theorem (Parseval's Theorem)

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Rayleigh Energy Theorem (Parseval's Theorem)

Theorem: For any ,

Real Exponents

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Real Exponents
The closest we can actually get to most real numbers is to compute arational number that is as close as we need. It can be shown that rational numbers are dense in the real numbers; that is, between every two real numbers there is a rational number, and between every two rational numbers is a real number. Anirrational number can be defined as any real number having a non-repeating decimal expansion. For example, is an irrational real number whose decimal expansion starts out as

Reconstruction from Samples--Pictorial Version

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Reconstruction from Samples--Pictorial Version
Figure A.1 shows how a sound is reconstructed from its samples. Each sample can be considered as specifying thescaling and location of a sinc function. The discrete-time signal being interpolated in the figure is . The sinc functions are drawn with dashed lines, and they sum to produce the solid curve. Note the ''Gibb's overshoot'' near the corners of this continuous rectangular pulse due to band-limiting.

Reconstruction from Samples--The Math

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Reconstruction from Samples--The Math
Let denote the th sample of the original sound , where is time in seconds. Thus, ranges over the integers, and is the sampling period in seconds. Thesampling rate in Hertz (Hz) is just the reciprocal of the sampling period,i.e.,

Recovering a Continuous-Time Signal from its Samples

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Recovering a Continuous-Time Signal from its Samples
Given samples of a properly band-limited signal, how do we reconstruct the original continuous waveform? I.e., given , how do we compute for any value of ?

Repeat Operator

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Repeat Operator
Like the operator, the operator maps a length signal to a length signal:

Sampled Sinusoids

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Sampled Sinusoids
In discrete-time audio processing, such as we must do on a computer, we work with samples of continuous-time signals. Let denote thesampling rate in Hz. For audio, we typically have kHz, since the audio band nominally extends to kHz. For compact discs (CDs), kHz (or very close to that--I once saw Sony device using a sampling rate of Hz), while for digital audio tape (DAT), kHz.

Shannon's Sampling Theorem

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Shannon's Sampling Theorem
Theorem. Let denote any continuous-time signal having a continuous Fourier transform

Shift Operator

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Shift Operator

Definition: The shift operator is defined by

Shift Theorem

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Shift Theorem

Theorem: For any and any integer ,

Sidebar on Mathematica

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Sidebar on Mathematica
Mathematica is a handy tool for cranking out any number of digits intranscendental numbers such as :
In[]: N[E,50] Out[]: 2.7182818284590452353602874713526624977572470937
Alternatively, we can compute for small :
In[]: (1+delta)^(1/delta) /. delta->0.001 Out[]: 2.716923932235594 In[]: (1+delta)^(1/delta) /. delta->0.0001 Out[]: 2.718145926824926 In[]: (1+delta)^(1/delta) /. delta->0.00001 Out[]: 2.718268237192297
What happens if we just go for it and set delta to zero?
In[]: (1+delta)^(1/delta) /. delta->0 1 Power::infy: Infinite expression - encountered. 0 Infinity::indt: ComplexInfinity Indeterminate expression 1 encountered. Indeterminate

Signal Metrics

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Signal Metrics
This section defines some useful functions of signals.
The mean of a signal (more precisely the ''sample mean'') is defined as its average value:

Signal Operators

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Signal Operators
It will be convenient in the Fourier theorems below to make use of the following signal operator definitions.

Signal Reconstruction from Projections

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Signal Reconstruction from Projections
We now know how to project a signal onto other signals. We now need to learn how to reconstruct a signal from its projections onto different vectors , . This will give us theinverse DFT operation (or the inverse of whatever transform we are working with).

Signals as Vectors

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Signals as Vectors
For the DFT, all signals and spectra are length . A length sequence can be denoted by , , where may be real () or complex (). We now wish to regard as avector ^6.1 in an dimensional vector space. That is, each sample is regarded as a coordinate in that space. A vector is mathematically a single point in -space represented by a list of coordinates called an -tuple. (The notation means the same thing as .) It can be interpreted geometrically as an arrow in -space from the origin to the point .

Sinusoids

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Sinusoids
A sinusoid is any function of time having the following form:

Sinusoids and Exponentials

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Sinusoids and Exponentials
This chapter provides an introduction to sinusoids, exponentials, complex sinusoids, , in-phase and quadrature sinusoidal components, theanalytic signal, positive and negative frequencies, constructive anddestructive interference, invariance of sinusoidal frequency in linear time-invariant systems, circular motion as the vector sum of in-phase and quadrature sinusoidal motions, sampled sinusoids, generating sampled sinusoids from powers of , and plot examples using Mathematica.

Sinusoids at the Same Frequency

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Sinusoids at the Same Frequency
An important property of sinusoids at a particular frequency is that they are closed with respect to addition. In other words, if you take a sinsusoid, make many copies of it, scale them all by different gains, delay them all by different amounts, and add them up, you always get a sinusoid at the same original frequency. This is a nontrivial property. It obviously holds for any constant signal (which we may regard as a sinusoid at frequency ), but it is not obvious for (see Fig. 5.2 and think about the sum of the two waveforms shown being precisely a sinusoid).

Special Case: The Mth Roots of Unity

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Special Case: The Mth Roots of Unity
If , we have

Specific DB Scales

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Specific DB Scales
Since we so often rescale our signals to suit various needs (avoiding overflow, reducing quantization noise, making a nicer plot, etc.), there seems to be little point in worrying about what the dB reference is--we simply choose it implicitly when we rescale to obtain signal values in the range we want to see. Nevertheless, a few specific dB scales are worth knowing about.

Spectral Phase

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Spectral Phase
As for the phase of the spectrum, what do we expect? We have chosen thesinusoid phase to be zero. The window is symmetric about its middle. Therefore, we expect a linear phase term with slope -(M-1)/2 samples. Also, the window transform has sidelobes which cause a phase of pi radians to switch in and out. Thus, we expect to see samples of a straight line with slope -15 across the main lobe of the window transform, together with a switching offset by pi in every other sidelobe away from the main lobe, starting with the immediately adjacent sidelobes.

Spectrum Analysis of a Sinusoid: Windowing, Zero-Padding, and the FFT

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Spectrum Analysis of a Sinusoid: Windowing, Zero-Padding, and the FFT
The examples below give a progression from the most simplistic analysis up to a proper practical treatment. Careful study of these examples will teach you a lot about how spectrum analysis is carried out on real data, and provide opportunities to see the Fourier theorems in action.

Stretch Operator

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Stretch Operator
Unlike all previous operators, the operator maps a length signal to a length signal, where and are integers. We use '''' instead of '''' as the time index to underscore this fact.

Stretch Theorem (Repeat Theorem)

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Stretch Theorem (Repeat Theorem)

Theorem: For all ,

Symmetry

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Symmetry
In the previous section, we found when is real. This fact is of high practical importance. It says that the spectrum of every real signal is Hermitian. Due to this symmetry, we may discard all negative-frequency spectral samples of a real signal and regenerate them later if needed from the positive-frequency samples. Also, spectral plots of real signals are normally displayed only for positive frequencies; e.g., spectra of sampled signals are normally plotted over the range Hz to Hz. On the other hand, the spectrum of a complex signal must be shown, in general, from to (or from to ), since the positive and negative frequency components of a complex signal are independent.

The Analytic Signal and Hilbert Transform Filters

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The Analytic Signal and Hilbert Transform Filters
A signal which has no negative-frequency components is called ananalytic signal.^5.6 Therefore, in continuous time, every analytic signal can be represented as

The BiQuad Section

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The BiQuad Section
The term ''biquad'' is short for ''bi-quadratic'', and is a common name for a two-pole, two-zero digital filter. Thetransfer function of a biquad can be defined as

The Complex Plane

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The Complex Plane

Figure 2.2:Plotting a complex number as a point in thecomplex plane.

The DFT

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The DFT
For a length complex sequence , , thediscrete Fourier transform (DFT) is defined by

The DFT and its Inverse

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The DFT and its Inverse
Let denote an -sample complex sequence, i.e., . Then the spectrum of is defined by the Discrete Fourier Transform (DFT):

The DFT Derived

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The DFT Derived
In this section, the Discrete Fourier Transform (DFT) will be derived.

Subsections
Geometric Series
Orthogonality of Sinusoids
Orthogonality of the DFT Sinusoids
Norm of the DFT Sinusoids
An Orthonormal Sinusoidal Set
The Discrete Fourier Transform (DFT)
Frequencies in the ''Cracks''
Normalized DFT

The DFT Matrix

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DFT Matrix
The following example reinforces the discussion of the DFT matrix. We can simply create the DFT matrix in Matlab by taking the FFT of the identity matrix. Then we show that multiplying by the DFT matrix is equivalent to the FFT:
>> eye(4) ans = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
>> S4 = fft(eye(4)) ans = 1.0000 1.0000 1.0000 1.0000
1.0000 0.0000 - 1.0000i -1.0000 0.0000 + 1.0000i 1.0000 -1.0000 1.0000 -1.0000
1.0000 0.0000 + 1.0000i -1.0000 0.0000 - 1.0000i

The Discrete Fourier Transform (DFT) Derived

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The Discrete Fourier Transform (DFT)
Given a signal , the spectrum is defined by

The Exponent Zero

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The Exponent Zero
What should be? Multiplying it by gives

The Fourier Theorems

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The Fourier Theorems
In this section the main Fourier theorems are stated and proved. It is no small matter how simple these theorems are in the DFT case relative to the other three cases (DTFT, Fourier transform, and Fourier series). When infinite summations or integrals are involved, the conditions for the existence of the Fourier transform can be quite difficult to characterize mathematically. Mathematicians have expended a considerable effort on such questions. By focusing primarily on the DFT case, we are able to study the essential concepts conveyed by the Fourier theorems without getting involved with mathematical difficulties.

The Fundamental Theorem of Algebra

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The Fundamental Theorem of Algebra
This is a very powerful algebraic tool. It says that given any polynomial

The Inner Product

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The Inner Product
The inner product (or ''dot product'') is an operation on two vectors which produces a scalar. Adding an inner product to a Banach space produces a Hilbert space (or ''inner product space''). There are many examples of Hilbert spaces, but we will only need for this course (complex length vectors with complex scalars).

The Length 2 DFT

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The Length 2 DFT
The length DFT is particularly simple, since the basissinusoids are real:

The Pythagorean Theorem in N-Space

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The Pythagorean Theorem in N-Space
In 2D, the Pythagorean Theorem says that when and are orthogonal, as in Fig. 6.8, (i.e., when the triangle formed by , , and , with translated to the tip of , is a right triangle), then we have

The Quadratic Formula

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The Quadratic Formula
The general second-order polynomial is

The Weierstrass (Polynomial) Approximation Theorem

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The Weierstrass (Polynomial) Approximation Theorem
Let be continuous on a real interval . Then for any , there exists an th-order polynomial , where depends on, such that

Transfer Function

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Transfer Function
The transfer function associated with any filter is defined as the transform of its impulse response. For the FIR filter we have

Triangle Difference Inequality

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Triangle Difference Inequality
A useful variation on the triangle inequality is that the length of any side of a triangle is greater than the absolute difference of the lengths of the other two sides:

Triangle Inequality

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Triangle Inequality
The triangle inequality states that the length of any side of a triangle is less than or equal to the sum of the lengths of the other two sides, with equality occurring only when the triangle degenerates to a line. In , this becomes

Two's Complement Fixed-Point Format

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Two's Complement Fixed-Point Format
In two's complement, numbers are negated by complementing the bit pattern and adding 1, with overflow ignored. From 0 to, positive numbers are assigned to binary values exactly as in one's complement. The remaining assignments (for the negative numbers) can be carried out using the two's complement negation rule. Regenerating the example in this way gives Table 4.4.

Vector Addition

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Vector Addition
Given two vectors in , say and , the vector sum is defined byelementwise addition. If we denote the sum by , then we have for .

Vector Cosine

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Vector Cosine
The Cauchy-Schwarz Inequality can be written

Vector Subtraction

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Vector Subtraction
Figure 6.7 illustrates the vector difference between and . From the coordinates, we compute .

What frequencies are representable by a geometric sequence?

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What frequencies are representable by a geometric sequence?
A natural question to investigate is what frequencies are possible. The angular step of the point along the unit circle in the complex plane is . Since , an angular step larger than , say is indistinguishable from the angular step. Therefore, we must restrict the angular step to a length range in order to avoid ambiguity.

When Do We Have to Swap Bytes When Changing Computers?

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When Do We Have to Swap Bytes When Changing Computers?
When moving a soundfile from one computer to another, such as from a ''PC'' to a ''Mac'' (Intel processor to Motorola processor), the bytes in each sound sample have to be swapped. This is because Motorola processors are big endian (bytes are numbered from ''left to right'' in a multi-byte word) while Intel processors are little endian. Any Mac program that supports a soundfile format native to PCs (such as .wav files) will swap the bytes for you. You only have to worry about swapping the bytes yourself when reading raw binary soundfiles from a foreign computer, or when digging the sound samples out an ''unsupported'' soundfile format yourself.

Why (Generalized) Complex Sinusoids are Important

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Why (Generalized) Complex Sinusoids are Important
As a preview of things to come, note that one signal^5.10 is projected onto another signal using an inner product. The inner product computes the coefficient of projection^5.11 of onto . If (a sampled, unit-amplitude, zero-phase, complex sinusoid), then the inner product computes the Discrete Fourier Transform (DFT), provided the frequencies are chosen to be . For the DFT, the inner product is specifically

Why Exponentials are Important

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Why Exponentials are Important
Exponential decay occurs naturally when a quantity is decaying at a rate which is proportional to how much is left. In nature, all linear resonators, such as musical instrument strings and woodwind bores, exhibit exponential decay in their response to a momentary excitation. As another example, reverberant energy in a room decays exponentially after the direct sound stops. Essentially all undriven oscillations decay exponentially (provided they are linear and time-invariant). Undriven means there is no ongoing source of driving energy. Examples of undriven oscillations include the vibrations of a tuning fork, struck or plucked strings, a marimba or xylophone bar, and so on. Examples of driven oscillations include horns, woodwinds, bowed strings, and voice. Driven oscillations must be periodic while undriven oscillations normally are not, except in idealized cases.

Why Sinusoids are Important

Sun, 01 Mar 1998 00:00:00 +0000

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Why Sinusoids are Important
Sinusoids are fundamental in a variety of ways.
One reason for the importance of sinusoids is that they are fundamental in physics. Anything that resonates or oscillates produces quasi-sinusoidal motion. See simple harmonic motion in any freshman physics text for an introduction to this topic.

Zero Padding

Sun, 01 Mar 1998 00:00:00 +0000

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Zero Padding

Definition: Zero padding consists of appending zeros to a signal. It maps a length signal to a length signal, but need not be an integer multiple of :

Zero Padding Theorem

Sun, 01 Mar 1998 00:00:00 +0000

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Zero Padding Theorem
A fundamental tool in practical spectrum analysis is zero padding. This theorem shows that zero padding in the time domain corresponds to ideal interpolation in the frequency domain:

AWG
Temperature	[ºC]
Material
	OUTPUT
Copper Diameter	[mm]
Copper Area	[mm²]
Resistance	[Ohm/m]

Dec	Hex	Char	Description	Dec	Hex	Char	Dec	Hex	Char	Dec	Hex	Char
0	0	NUL	null	32	20		64	40	@	96	60	`
1	1	SOH	start of heading	33	21	!	65	41	A	97	61	a
2	2	STX	start of text	34	22	"	66	42	B	98	62	b
3	3	ETX	end of text	35	23	#	67	43	C	99	63	c
4	4	EOT	end of transmission	36	24	$	68	44	D	100	64	d
5	5	ENQ	enquiry	37	25	%	69	45	E	101	65	e
6	6	ACK	acknowledge	38	26	&	70	46	F	102	66	f
7	7	BEL	bell	39	27	'	71	47	G	103	67	g
8	8	BS	backspace	40	28	(	72	48	H	104	68	h
9	9	TAB	horizontal tab	41	29	)	73	49	I	105	69	i
10	A	LF	NL line feed, new line	42	2A	*	74	4A	J	106	6A	j
11	B	VT	vertical tab	43	2B	+	75	4B	K	107	6B	k
12	C	FF	NP form feed, new page	44	2C	,	76	4C	L	108	6C	l
13	D	CR	carriage return	45	2D	-	77	4D	M	109	6D	m
14	E	SO	shift out	46	2E	.	78	4E	N	110	6E	n
15	F	SI	shift in	47	2F	/	79	4F	O	111	6F	o
16	10	DLE	data link escape	48	30	0	80	50	P	112	70	p
17	11	DC1	device control 1	49	31	1	81	51	Q	113	71	q
18	12	DC2	device control 2	50	32	2	82	52	R	114	72	r
19	13	DC3	device control 3	51	33	3	83	53	S	115	73	s
20	14	DC4	device control 4	52	34	4	84	54	T	116	74	t
21	15	NAK	negative acknowledge	53	35	5	85	55	U	117	75	u
22	16	SYN	synchronous idle	54	36	6	86	56	V	118	76	v
23	17	ETB	end of transmission block	55	37	7	87	57	W	119	77	w
24	18	CAN	cancel	56	38	8	88	58	X	120	78	x
25	19	EM	end of medium	57	39	9	89	59	Y	121	79	y
26	1A	SUB	substitute	58	3A	:	90	5A	Z	122	7A	z
27	1B	ESC	escape	59	3B	;	91	5B	[	123	7B	{
28	1C	FS	file separator	60	3C	<	92	5C	\	124	7C	\|
29	1D	GS	group separator	61	3D	=	93	5D	]	125	7D	}
30	1E	RS	record separator	62	3E	>	94	5E	^	126	7E	~
31	1F	US	unit separator	63	3F	?	95	5F	_	127	7F	DEL