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Continuous and discrete time signals and systems PDF

879 Pages·2007·6.04 MB·English
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P1:RPU/... P2:RPU/... QC:RPU/... T1:RPU CUUK852-Mandal&Asif May28,2007 14:22 ContinuousandDiscreteTimeSignalsandSystems Signalsandsystemsisacoretopicforelectricalandcomputerengineers.This textbookpresentsanintroductiontothefundamentalconceptsofcontinuous- time(CT)anddiscrete-time(DT)signalsandsystems,treatingthemseparately in a pedagogical and self-contained manner. Emphasis is on the basic sig- nalprocessingprinciples,withunderlyingconceptsillustratedusingpractical examplesfromsignalprocessingandmultimediacommunications.Thetextis dividedintothreeparts.PartIpresentstwointroductorychaptersonsignalsand systems.PartIIcoversthetheories,techniques,andapplicationsofCTsignals andsystemsandPartIIIdiscussesthesetopicsforDTsignalsandsystems,so thatthetwocanbetaughtindependentlyortogether.Thefocusthroughoutis principallyonlineartimeinvariantsystems.AccompanyingthebookisaCD- ROMcontainingMATLAB codeforrunningillustrativesimulationsincluded inthetext;datafilescontainingaudioclips,imagesandinteractiveprograms usedinthetext,andtwoanimationsexplainingtheconvolutionoperation.With over300illustrations,287workedexamplesand409homeworkproblems,this textbookisanidealintroductiontothesubjectforundergraduatesinelectrical and computer engineering. Further resources, including solutions for instruc- tors,areavailableonlineatwww.cambridge.org/9780521854559. Mrinal Mandal is an associate professor at the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada. His main research interests include multimedia signal processing, medical image and videoanalysis,imageandvideocompression,andVLSIarchitecturesforreal- timesignalandimageprocessing. AmirAsifisanassociateprofessorattheDepartmentofComputerScienceand Engineering,YorkUniversity,Toronto,Canada.Hisprincipalresearchareaslie instatisticalsignalprocessingwithapplicationsinimageandvideoprocessing, multimediacommunications,andbioinformatics,withparticularfocusonvideo compression,arrayimagingdetection,genomicsignalprocessing,andblock- bandedmatrixtechnologies. i P1:RPU/... P2:RPU/... QC:RPU/... T1:RPU CUUK852-Mandal&Asif May28,2007 14:22 ii P1:RPU/... P2:RPU/... QC:RPU/... T1:RPU CUUK852-Mandal&Asif May28,2007 14:22 Continuous and Discrete Time Signals and Systems Mrinal Mandal UniversityofAlberta,Edmonton,Canada and Amir Asif YorkUniversity,Toronto,Canada iii P1:RPU/... P2:RPU/... QC:RPU/... T1:RPU CUUK852-Mandal&Asif May28,2007 14:22 CAMBRIDGE UNIVERSITY PRESS Cambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,Sa˜oPaulo CambridgeUniversityPress TheEdinburghBuilding,CambridgeCB28RU,UK PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork www.cambridge.org Informationonthistitle:www.cambridge.org/9780521854559 C CambridgeUniversityPress2007 (cid:2) Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithout thewrittenpermissionofCambridgeUniversityPress. Firstpublished2007 PrintedintheUnitedKingdomattheUniversityPress,Cambridge AcatalogrecordforthispublicationisavailablefromtheBritishLibrary ISBN-13 978-0-521-85455-9hardback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofURLsfor externalorthird-partyinternetwebsitesreferredtointhispublication,anddoesnotguaranteethat anycontentonsuchwebsitesis,orwillremain,accurateorappropriate. AllmaterialcontainedwithintheCD-ROMisprotectedbycopyrightandotherintellectual propertylaws.ThecustomeracquiresonlytherighttousetheCD-ROManddoesnotacquireany otherrights,expressorimplied,unlessthesearestatedexplicitlyinaseparatelicence. Totheextentpermittedbyapplicablelaw,CambridgeUniversityPressisnotliablefordirect damagesorlossofanykindresultingfromtheuseofthisproductorfromerrorsorfaults containedinit,andineverycaseCambridgeUniversityPress’sliabilityshallbelimitedtothe amountactuallypaidbythecustomerfortheproduct. iv P1:RPU/... P2:RPU/... QC:RPU/... T1:RPU CUUK852-Mandal&Asif May28,2007 14:22 Contents Preface pagexi PartI Introductiontosignalsandsystems 1 1 Introductiontosignals 3 1.1 Classificationofsignals 5 1.2 Elementarysignals 25 1.3 Signaloperations 35 1.4 SignalimplementationwithMATLAB 47 1.5 Summary 51 Problems 53 2 Introductiontosystems 62 2.1 Examplesofsystems 63 2.2 Classificationofsystems 72 2.3 Interconnectionofsystems 90 2.4 Summary 93 Problems 94 PartII Continuous-timesignalsandsystems 101 3 Time-domainanalysisofLTICsystems 103 3.1 RepresentationofLTICsystems 103 3.2 RepresentationofsignalsusingDiracdeltafunctions 112 3.3 Impulseresponseofasystem 113 3.4 Convolutionintegral 116 3.5 Graphicalmethodforevaluatingtheconvolutionintegral 118 3.6 Propertiesoftheconvolutionintegral 125 3.7 ImpulseresponseofLTICsystems 127 3.8 ExperimentswithMATLAB 131 3.9 Summary 135 Problems 137 v P1:RPU/... P2:RPU/... QC:RPU/... T1:RPU CUUK852-Mandal&Asif May28,2007 14:22 vi Contents 4 SignalrepresentationusingFourierseries 141 4.1 Orthogonalvectorspace 142 4.2 Orthogonalsignalspace 143 4.3 Fourierbasisfunctions 149 4.4 TrigonometricCTFS 153 4.5 ExponentialFourierseries 163 4.6 PropertiesofexponentialCTFS 169 4.7 ExistenceofFourierseries 177 4.8 ApplicationofFourierseries 179 4.9 Summary 182 Problems 184 5 Continuous-timeFouriertransform 193 5.1 CTFTforaperiodicsignals 193 5.2 ExamplesofCTFT 196 5.3 InverseFouriertransform 209 5.4 Fouriertransformofreal,even,andoddfunctions 211 5.5 PropertiesoftheCTFT 216 5.6 ExistenceoftheCTFT 231 5.7 CTFTofperiodicfunctions 233 5.8 CTFScoefficientsassamplesofCTFT 235 5.9 LTICsystemsanalysisusingCTFT 237 5.10 MATLAB exercises 246 5.11 Summary 251 Problems 253 6 Laplacetransform 261 6.1 Analyticaldevelopment 262 6.2 UnilateralLaplacetransform 266 6.3 InverseLaplacetransform 273 6.4 PropertiesoftheLaplacetransform 276 6.5 Solutionofdifferentialequations 288 6.6 Characteristicequation,zeros,andpoles 293 6.7 PropertiesoftheROC 295 6.8 StableandcausalLTICsystems 298 6.9 LTICsystemsanalysisusingLaplacetransform 305 6.10 Blockdiagramrepresentations 307 6.11 Summary 311 Problems 313 7 Continuous-timefilters 320 7.1 Filterclassification 321 7.2 Non-idealfiltercharacteristics 324 7.3 DesignofCTlowpassfilters 327 P1:RPU/... 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T1:RPU CUUK852-Mandal&Asif May28,2007 14:22 vii Contents 7.4 Frequencytransformations 352 7.5 Summary 364 Problems 365 8 CasestudiesforCTsystems 368 8.1 Amplitudemodulationofbasebandsignals 369 8.2 Mechanicalspringdampersystem 374 8.3 Armature-controlleddcmotor 377 8.4 Immunesysteminhumans 383 8.5 Summary 388 Problems 388 PartIII Discrete-timesignalsandsystems 391 9 Samplingandquantization 393 9.1 Idealimpulse-trainsampling 395 9.2 Practicalapproachestosampling 405 9.3 Quantization 410 9.4 Compactdisks 413 9.5 Summary 415 Problems 416 10 Time-domainanalysisofdiscrete-timesystemssystems 422 10.1 Finite-differenceequationrepresentation ofLTIDsystems 423 10.2 RepresentationofsequencesusingDiracdeltafunctions 426 10.3 Impulseresponseofasystem 427 10.4 Convolutionsum 430 10.5 Graphicalmethodforevaluatingtheconvolutionsum 432 10.6 Periodicconvolution 439 10.7 Propertiesoftheconvolutionsum 448 10.8 ImpulseresponseofLTIDsystems 451 10.9 ExperimentswithMATLAB 455 10.10 Summary 459 Problems 460 11 Discrete-timeFourierseriesandtransform 464 11.1 Discrete-timeFourierseries 465 11.2 Fouriertransformforaperiodicfunctions 475 11.3 ExistenceoftheDTFT 482 11.4 DTFTofperiodicfunctions 485 11.5 PropertiesoftheDTFTandtheDTFS 491 11.6 FrequencyresponseofLTIDsystems 506 11.7 Magnitudeandphasespectra 507 P1:RPU/... 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T1:RPU CUUK852-Mandal&Asif May28,2007 14:22 viii Contents 11.8 Continuous-anddiscrete-timeFouriertransforms 514 11.9 Summary 517 Problems 520 12 DiscreteFouriertransform 525 12.1 ContinuoustodiscreteFouriertransform 526 12.2 DiscreteFouriertransform 531 12.3 SpectrumanalysisusingtheDFT 538 12.4 PropertiesoftheDFT 547 12.5 ConvolutionusingtheDFT 550 12.6 FastFouriertransform 553 12.7 Summary 559 Problems 560 13 Thez-transform 565 13.1 Analyticaldevelopment 566 13.2 Unilateralz-transform 569 13.3 Inversez-transform 574 13.4 Propertiesofthez-transform 582 13.5 Solutionofdifferenceequations 594 13.6 z-transferfunctionofLTIDsystems 596 13.7 RelationshipbetweenLaplaceandz-transforms 599 13.8 Stabiltyanalysisinthez-domain 601 13.9 Frequency-responsecalculationinthez-domain 606 13.10 DTFTandthez-transform 607 13.11 ExperimentswithMATLAB 609 13.12 Summary 614 Problems 616 14 Digitalfilters 621 14.1 Filterclassification 622 14.2 FIRandIIRfilters 625 14.3 Phaseofadigitalfilter 627 14.4 Idealversusnon-idealfilters 632 14.5 Filterrealization 638 14.6 FIRfilters 639 14.7 IIRfilters 644 14.8 Finiteprecisioneffect 651 14.9 MATLAB examples 657 14.10 Summary 658 Problems 660 15 FIRfilterdesign 665 15.1 Lowpassfilterdesignusingwindowingmethod 666 15.2 Designofhighpassfiltersusingwindowing 684 15.3 Designofbandpassfiltersusingwindowing 688 P1:RPU/... 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T1:RPU CUUK852-Mandal&Asif May28,2007 14:22 ix Contents 15.4 Designofabandstopfilterusingwindowing 691 15.5 OptimalFIRfilters 693 15.6 MATLAB examples 700 15.7 Summary 707 Problems 709 16 IIRfilterdesign 713 16.1 IIRfilterdesignprinciples 714 16.2 Impulseinvariance 715 16.3 Bilineartransformation 728 16.4 Designinghighpass,bandpass,andbandstopIIRfilters 734 16.5 IIRandFIRfilters 737 16.6 Summary 741 Problems 742 17 Applicationsofdigitalsignalprocessing 746 17.1 Spectralestimation 746 17.2 Digitalaudio 754 17.3 Audiofiltering 759 17.4 Digitalaudiocompression 765 17.5 Digitalimages 771 17.6 Imagefiltering 777 17.7 Imagecompression 782 17.8 Summary 789 Problems 789 AppendixA Mathematicalpreliminaries 793 A.1 Trigonometricidentities 793 A.2 Powerseries 794 A.3 Seriessummation 794 A.4 Limitsanddifferentialcalculus 795 A.5 Indefiniteintegrals 795 AppendixB Introductiontothecomplex-numbersystem 797 B.1 Real-numbersystem 797 B.2 Complex-numbersystem 798 B.3 Graphicalinterpertationofcomplexnumbers 801 B.4 Polarrepresentationofcomplexnumbers 801 B.5 Summary 805 Problems 805 AppendixC Linearconstant-coefficientdifferentialequations 806 C.1 Zero-inputresponse 807 C.2 Zero-stateresponse 810 C.3 Completeresponse 813 P1:RPU/... P2:RPU/... QC:RPU/... T1:RPU CUUK852-Mandal&Asif May28,2007 14:22 x Contents AppendixD Partialfractionexpansion 814 D.1 Laplacetransform 814 D.2 Continuous-timeFouriertransform 822 D.3 Discrete-timeFouriertransform 825 D.4 Thez-transform 826 AppendixE IntroductiontoMATLAB 829 E.1 Introduction 829 E.2 EnteringdataintoMATLAB 831 E.3 Controlstatements 838 E.4 Elementarymatrixoperations 840 E.5 Plottingfunctions 842 E.6 CreatingMATLAB functions 846 E.7 Summary 847 AppendixF AbouttheCD 848 F.1 Interactiveenvironment 848 F.2 Data 853 F.3 MATLAB codes 854 Bibliography 858 Index 860

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