A PRACTICAL APPROACH TO SIGNALS AND SYSTEMS

400 Pages·2008·2.65 MB·English

by  D. Sundararajan

A PRACTICAL APPROACH
TO SIGNALS AND SYSTEMS
D.Sundararajan
JohnWiley&Sons(Asia)PteLtd

A PRACTICAL APPROACH
TO SIGNALS AND SYSTEMS

A PRACTICAL APPROACH
TO SIGNALS AND SYSTEMS
D.Sundararajan
JohnWiley&Sons(Asia)PteLtd
Copyright©2008 JohnWiley&Sons(Asia)PteLtd,2ClementiLoop,#02-01,
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LibraryofCongressCataloging-in-PublicationData
Sundararajan,D.
Practicalapproachtosignalsandsystems/D.Sundararajan.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-82353-8(cloth)
1.Signaltheory(Telecommunication) 2.Signalprocessing. 3.Systemanalysis.I.Title.
TKTK5102.9.S7962008
621.382’23–dc22
2008012023
ISBN978-0-470-82353-8(HB)
Typesetin11/13ptTimesbyThomsonDigital,Noida,India.
PrintedandboundinSingaporebyMarkonoPrintMediaPteLtd,Singapore.
Thisbookisprintedonacid-freepaperresponsiblymanufacturedfromsustainableforestryinwhichatleasttwo
treesareplantedforeachoneusedforpaperproduction.
Contents
Preface xiii
Abbreviations xv
1 Introduction 1
1.1 TheOrganizationofthisBook 1
2 DiscreteSignals 5
2.1 ClassificationofSignals 5
2.1.1 Continuous,DiscreteandDigitalSignals 5
2.1.2 PeriodicandAperiodicSignals 7
2.1.3 EnergyandPowerSignals 7
2.1.4 Even-andOdd-symmetricSignals 8
2.1.5 CausalandNoncausalSignals 10
2.1.6 DeterministicandRandomSignals 10
2.2 BasicSignals 11
2.2.1 Unit-impulseSignal 11
2.2.2 Unit-stepSignal 12
2.2.3 Unit-rampSignal 13
2.2.4 SinusoidsandExponentials 13
2.3 SignalOperations 20
2.3.1 TimeShifting 21
2.3.2 TimeReversal 21
2.3.3 TimeScaling 22
2.4 Summary 23
FurtherReading 23
Exercises 23
3 ContinuousSignals 29
3.1 ClassificationofSignals 29
3.1.1 ContinuousSignals 29
3.1.2 PeriodicandAperiodicSignals 30
3.1.3 EnergyandPowerSignals 31
vi Contents
3.1.4 Even-andOdd-symmetricSignals 31
3.1.5 CausalandNoncausalSignals 33
3.2 BasicSignals 33
3.2.1 Unit-stepSignal 33
3.2.2 Unit-impulseSignal 34
3.2.3 Unit-rampSignal 42
3.2.4 Sinusoids 43
3.3 SignalOperations 45
3.3.1 TimeShifting 45
3.3.2 TimeReversal 46
3.3.3 TimeScaling 47
3.4 Summary 48
FurtherReading 48
Exercises 48
4 Time-domainAnalysisofDiscreteSystems 53
4.1 DifferenceEquationModel 53
4.1.1 SystemResponse 55
4.1.2 ImpulseResponse 58
4.1.3 Characterization of Systems by their Responses to Impulse
andUnit-stepSignals 60
4.2 ClassificationofSystems 61
4.2.1 LinearandNonlinearSystems 61
4.2.2 Time-invariantandTime-varyingSystems 62
4.2.3 CausalandNoncausalSystems 63
4.2.4 InstantaneousandDynamicSystems 64
4.2.5 InverseSystems 64
4.2.6 ContinuousandDiscreteSystems 64
4.3 Convolution–SummationModel 64
4.3.1 PropertiesofConvolution–Summation 67
4.3.2 TheDifferenceEquationandConvolution–Summation 68
4.3.3 ResponsetoComplexExponentialInput 69
4.4 SystemStability 71
4.5 RealizationofDiscreteSystems 72
4.5.1 DecompositionofHigher-orderSystems 73
4.5.2 FeedbackSystems 74
4.6 Summary 74
FurtherReading 75
Exercises 75
Contents vii
5 Time-domainAnalysisofContinuousSystems 79
5.1 ClassificationofSystems 80
5.1.1 LinearandNonlinearSystems 80
5.1.2 Time-invariantandTime-varyingSystems 81
5.1.3 CausalandNoncausalSystems 82
5.1.4 InstantaneousandDynamicSystems 83
5.1.5 Lumped-parameterandDistributed-parameterSystems 83
5.1.6 InverseSystems 83
5.2 DifferentialEquationModel 83
5.3 Convolution-integralModel 85
5.3.1 PropertiesoftheConvolution-integral 87
5.4 SystemResponse 88
5.4.1 ImpulseResponse 88
5.4.2 ResponsetoUnit-stepInput 89
5.4.3 Characterization of Systems by their Responses to Impulse
andUnit-stepSignals 91
5.4.4 ResponsetoComplexExponentialInput 92
5.5 SystemStability 93
5.6 RealizationofContinuousSystems 94
5.6.1 DecompositionofHigher-orderSystems 94
5.6.2 FeedbackSystems 95
5.7 Summary 96
FurtherReading 97
Exercises 97
6 TheDiscreteFourierTransform 101
6.1 TheTime-domainandtheFrequency-domain 101
6.2 FourierAnalysis 102
6.2.1 VersionsofFourierAnalysis 104
6.3 TheDiscreteFourierTransform 104
6.3.1 The Approximation of Arbitrary Waveforms with a Finite
NumberofSamples 104
6.3.2 TheDFTandtheIDFT 105
6.3.3 DFTofSomeBasicSignals 107
6.4 PropertiesoftheDiscreteFourierTransform 110
6.4.1 Linearity 110
6.4.2 Periodicity 110
6.4.3 CircularShiftofaSequence 110
6.4.4 CircularShiftofaSpectrum 111
6.4.5 Symmetry 111
6.4.6 CircularConvolutionofTime-domainSequences 112