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Digital Signal Processing 4ed Proakis.pdf

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    Cover
    Table of Contents
    1. Introduction
    2. Discrete-Time Signals and Systems
    3. The z-Transform and Its Application to the Analysis of LTI Systems
    4. Frequency Analysis of Signals
    5. Frequency-Domain Analysis of LTI Systems
    6. Sampling and Reconstruction of Signals
    7. The Discrete Fourier Transform: Its Properties and Applications
    8. Efficient Computation of the DFT: Fast Fourier Transform Algorithms
    9. Implementation of Discrete-Time Systems
    10. Design of Digital Filters
    11. Multirate Digital Signal Processing
    12. Linear Prediction and Optimum Linear Filters
    13. Adaptive Filters
    14. Appendix: Random Number Generators
    15. Appendix: Tables of Transition Coefficients for the Design of Lnear-Phase FIR Filters
    16. References and Bibliography
    Index
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    Digital Signal ProcessingJohn G. Proakis Dimitris K. ManolakisFourth Edition
    Pearson Education LimitedEdinburgh GateHarlowEssex CM20 2JEEngland and Associated Companies throughout the worldVisit us on the World Wide Web at: www.pearsoned.co.uk© Pearson Education Limited 2014 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS.All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affi liation with or endorsement of this book by such owners. British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library Printed in the United States of AmericaISBN 10: 1-292-02573-5ISBN 13: 978-1-292-02573-5ISBN 10: 1-292-02573-5ISBN 13: 978-1-292-02573-5
    Table of ContentsPEARSON CUSTOM LIBRARY I1. Introduction11John G. Proakis/Dimitris G. Manolakis2. Discrete-Time Signals and Systems4343John G. Proakis/Dimitris G. Manolakis3. The z-Transform and Its Application to the Analysis of LTI Systems151151John G. Proakis/Dimitris G. Manolakis4. Frequency Analysis of Signals229229John G. Proakis/Dimitris G. Manolakis5. Frequency-Domain Analysis of LTI Systems307307John G. Proakis/Dimitris G. Manolakis6. Sampling and Reconstruction of Signals395395John G. Proakis/Dimitris G. Manolakis7. The Discrete Fourier Transform: Its Properties and Applications461461John G. Proakis/Dimitris G. Manolakis8. Efficient Computation of the DFT: Fast Fourier Transform Algorithms523523John G. Proakis/Dimitris G. Manolakis9. Implementation of Discrete-Time Systems577577John G. Proakis/Dimitris G. Manolakis10. Design of Digital Filters669669John G. Proakis/Dimitris G. Manolakis11. Multirate Digital Signal Processing767767John G. Proakis/Dimitris G. Manolakis12. Linear Prediction and Optimum Linear Filters841841John G. Proakis/Dimitris G. Manolakis13. Adaptive Filters899899John G. Proakis/Dimitris G. Manolakis
    II14. Appendix: Random Number Generators981981John G. Proakis/Dimitris G. Manolakis15. Appendix: Tables of Transition Coefficients for the Design of Lnear-Phase FIR Filters987987John G. Proakis/Dimitris G. Manolakis16. References and Bibliography993993John G. Proakis/Dimitris G. Manolakis10071007Index
    IntroductionDigitalsignalprocessingisanareaofscienceandengineeringthathasdevelopedrapidlyoverthepast40years.Thisrapiddevelopmentisaresultofthesignificantadvancesindigitalcomputertechnologyandintegrated-circuitfabrication.Thedig-italcomputersandassociateddigitalhardwareoffourdecadesagowererelativelylargeandexpensiveand,asaconsequence,theirusewaslimitedtogeneral-purposenon-real-time(off-line)scientificcomputationsandbusinessapplications.Therapiddevelopmentsinintegrated-circuittechnology,startingwithmedium-scaleintegra-tion(MSI)andprogressingtolarge-scaleintegration(LSI),andnow,very-large-scaleintegration(VLSI)ofelectroniccircuitshasspurredthedevelopmentofpowerful,smaller,faster,andcheaperdigitalcomputersandspecial-purposedigitalhardware.Theseinexpensiveandrelativelyfastdigitalcircuitshavemadeitpossibletoconstructhighlysophisticateddigitalsystemscapableofperformingcomplexdigitalsignalpro-cessingfunctionsandtasks,whichareusuallytoodifficultand/ortooexpensivetobeperformedbyanalogcircuitryoranalogsignalprocessingsystems.Hencemanyofthesignalprocessingtasksthatwereconventionallyperformedbyanalogmeansarerealizedtodaybylessexpensiveandoftenmorereliabledigitalhardware.Wedonotwishtoimplythatdigitalsignalprocessingisthepropersolutionforallsignalprocessingproblems.Indeed,formanysignalswithextremelywideband-widths,real-timeprocessingisarequirement.Forsuchsignals,analogor,perhaps,opticalsignalprocessingistheonlypossiblesolution.However,wheredigitalcir-cuitsareavailableandhavesufficientspeedtoperformthesignalprocessing,theyareusuallypreferable.Notonlydodigitalcircuitsyieldcheaperandmorereliablesystemsforsignalprocessing,theyhaveotheradvantagesaswell.Inparticular,digitalprocessinghardwareallowsprogrammableoperations.Throughsoftware,onecanmoreeas-From Chapter 1 ofDigital Signal Processing:Principles,Algorithms,and Applications,Fourth Edition.John G.Proakis,Dimitris G.Manolakis.Copyright © 2007 by Pearson Education,Inc.All rights reserved.1
    ilymodifythesignalprocessingfunctionstobeperformedbythehardware.Thusdigitalhardwareandassociatedsoftwareprovideagreaterdegreeofflexibilityinsystemdesign.Also,thereisoftenahigherorderofprecisionachievablewithdigitalhardwareandsoftwarecomparedwithanalogcircuitsandanalogsignalprocessingsystems.Forallthesereasons,therehasbeenanexplosivegrowthindigitalsignalprocessingtheoryandapplicationsoverthepastthreedecades.Signals,Systems,andSignalProcessingAsignalisdefinedasanyphysicalquantitythatvarieswithtime,space,oranyotherindependentvariableorvariables.Mathematically,wedescribeasignalasafunctionofoneormoreindependentvariables.Forexample,thefunctionss1(t)=5ts2(t)=20t2describetwosignals,onethatvarieslinearlywiththeindependentvariablet(time)andasecondthatvariesquadraticallywitht.Asanotherexample,considerthefunctions(x,y)=3x+2xy+10y2Thisfunctiondescribesasignaloftwoindependentvariablesxandythatcouldrepresentthetwospatialcoordinatesinaplane.IntroductionWe begin by introducing some of with the process of converting an analog signal to digital form suitable for digital processing. As we shall see, digital processing of analog signals has some drawbacks. First, and foremost, conversion of an analog sig-nal to digital form, accomplished by sampling the signal and quantizing the samples, results in a distortion that prevents us from reconstructing the original analog signal from the quantized samples. Control of the amount of this distortion is achieved by proper choice of the sampling rate and the precision in the quantization process. Second, there are finite precision effectsthat must be considered in the digital pro-cessing of the quantized samples. (1.2)1(1.1)The signals described by (1.1) and (1.2) belong to a class of signals that are pre-cisely defined by specifying the functional dependence on the independent variable. However, there are cases where such a functional relationship is unknown or too highly complicated to be of any practical use.For example, a speech signal (see Fig. 1.1) cannot be described functionally by expressions such as (1.1). In general, a segment of speech may be represented to2
    Exampleofaspeechsignal.ahighdegreeofaccuracyasasumofseveralsinusoidsofdifferentamplitudesandfrequencies,thatis,asNi=1Ai(t)sin[2πFi(t)t+θi(t)]where{Ai(t)},{Fi(t)},and{θi(t)}arethesetsof(possiblytime-varying)amplitudes,frequencies,andphases,respectively,ofthesinusoids.Infact,onewaytointerprettheinformationcontentormessageconveyedbyanyshorttimesegmentofthespeechsignalistomeasuretheamplitudes,frequencies,andphasescontainedintheshorttimesegmentofthesignal.Anotherexampleofanaturalsignalisanelectrocardiogram(ECG).Suchasignalprovidesadoctorwithinformationabouttheconditionofthepatient’sheart.Similarly,anelectroencephalogram(EEG)signalprovidesinformationabouttheactivityofthebrain.Speech,electrocardiogram,andelectroencephalogramsignalsareexamplesofinformation-bearingsignalsthatevolveasfunctionsofasingleindependentvariable,namely,time.Anexampleofasignalthatisafunctionoftwoindependentvariablesisanimagesignal.Theindependentvariablesinthiscasearethespatialcoordinates.Thesearebutafewexamplesofthecountlessnumberofnaturalsignalsencounteredinpractice.Associatedwithnaturalsignalsarethemeansbywhichsuchsignalsaregener-ated.Forexample,speechsignalsaregeneratedbyforcingairthroughthevocalcords.Imagesareobtainedbyexposingaphotographicfilmtoasceneoranobject.Thussignalgenerationisusuallyassociatedwithasystemthatrespondstoastimulusorforce.Inaspeechsignal,thesystemconsistsofthevocalcordsandthevocaltract,alsocalledthevocalcavity.Thestimulusincombinationwiththesystemiscalledasignalsource.Thuswehavespeechsources,imagessources,andvariousothertypesofsignalsources.Asystemmayalsobedefinedasaphysicaldevicethatperformsanoperationonasignal.Forexample,afilterusedtoreducethenoiseandinterferencecorruptingadesiredinformation-bearingsignaliscalledasystem.Inthiscasethefilterperformssomeoperation(s)onthesignal,whichhastheeffectofreducing(filtering)thenoiseandinterferencefromthedesiredinformation-bearingsignal.IntroductionFigure1.1(1.3)3
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