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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.
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Continuous and Discrete
Time Signals and Systems
Mrinal Mandal
UniversityofAlberta,Edmonton,Canada
and
Amir Asif
YorkUniversity,Toronto,Canada
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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
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externalorthird-partyinternetwebsitesreferredtointhispublication,anddoesnotguaranteethat
anycontentonsuchwebsitesis,orwillremain,accurateorappropriate.
AllmaterialcontainedwithintheCD-ROMisprotectedbycopyrightandotherintellectual
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otherrights,expressorimplied,unlessthesearestatedexplicitlyinaseparatelicence.
Totheextentpermittedbyapplicablelaw,CambridgeUniversityPressisnotliablefordirect
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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
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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
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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
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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
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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
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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
