Signals and systems

1169 Pages·2014·9.728 MB·English

by  Nahvi, Mahmood

Nahvi-80709 book December13,2012 16:23
Signals and
Systems
Mahmood Nahvi
EmeritusProfessorofElectricalEngineering
CaliforniaPolytechnicStateUniversity
SanLuisObispo,California
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Nahvi-80709 book December13,2012 16:23
SIGNALSANDSYSTEMS
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ABOUT THE AUTHOR
MahmoodNahviisemeritusprofessorofelectricalengineeringatCaliforniaPolytech-
nicStateUniversity(CalPoly)inSanLuisObispo,California.HeearnedB.Sc.,M.Sc.,
andPh.D.degreesinelectricalengineering,andhasmorethan50yearsofeducational,
academic,research,andindustrialexperienceinthisfield.Hehastaughtundergraduate
andgraduatecoursesonvarioussubjectsincludingelectriccircuits,electronics,signals
andsystems,electromagnetics,randomsignalsandnoise,digitalsignalandimagepro-
cessing, and communications and control. Prior to joining the faculty at Cal Poly, he
heldpositionsasaguestprofessorandresearchscientistattheUniversityofStuttgartin
Germany,workingonsignalprocessinginspacecommunicationsystems,satellitemi-
crowaveranging,andsyntheticapertureradarprojectsfortheEuropeanSpaceAgency.
Inaddition,hewasafoundingfacultymember,professor,anddepartmentchairatSharif
University of Technology (former Aria-Mehr) in Teheran, Iran; a visiting professor at
MIT; and a research scientist at UCLA, the Laboratory for Neural Control at the Na-
tional Institutes of Health, and the Max-Planck Institute for Biological Cybernetics in
Tu¨bingen,Germany.HeisaseniormemberoftheInstituteofElectricalandElectronics
Engineers(IEEE).
Dr.Nahvi’sareasofspecialinterestandexpertiseincludenetworktheory,control
theory, adaptation and learning in synthetic and living systems, communication and
control in living systems, neural networks for pattern recognition and motor control,
satellitecommunication,digitalsignalandimageprocessing,andengineeringeducation.
In the area of engineering education, he has developed computer modules for electric
circuits,signals,andsystemsthatimprovetheteachingandlearningofthefundamentals
of electrical engineering. He is coauthor of Electric Circuits and Electromagnetics in
Schaum’sOutlineSeriespublishedbyMcGraw-Hill.
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Thisbookisdedicatedtothememoryof
JanabNahvi
humanist,scholar,andteacher.
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BRIEF CONTENTS
Preface xvii
1 IntroductiontoSignals 1
2 Sinusoids 121
3 Systems,Linearity,andTimeInvariance 157
4 Superposition,Convolution,andCorrelation 203
5 DifferentialEquationsandLTISystems 259
6 TheLaplaceTransformandItsApplications 313
7 FourierSeries 377
8 FourierTransform 427
9 SystemFunction,theFrequencyResponse,andAnalogFilters 487
10 Time-DomainSamplingandReconstruction 623
11 Discrete-TimeSignals 683
12 LinearTime-InvariantDiscrete-TimeSystems 733
13 DiscreteConvolution 763
14 LTIDifferenceEquations 797
15 Thez-TransformandItsApplications 827
16 Discrete-TimeFourierTransform 881
17 DiscreteFourierTransform 947
18 SystemFunction,theFrequencyResponse,andDigitalFilters 1005
Appendix ElectricCircuits 1093
Index 1107
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CONTENTS
Preface xvii 1.20 WeightedIntegration 68
1.21 WindowAveraging 71
1.22 DifferentiationandDifferences 73
Chapter 1
IntroductiontoSignals 1 1.23 ConcludingRemarks 76
IntroductionandSummary 2 1.24 Problems 76
1.1 DiscreteVersusContinuous; 1.25 Project1:BinarySignalinNoise 116
DigitalVersusAnalog 3 1.26 Project2:SignalsStoredas
1.2 DeterministicVersusRandom 5 ComputerDataFiles 120
1.3 ExamplesofNaturaland Chapter 2
SocietalSignals 6
Sinusoids 121
1.4 VoiceandSpeechSignals 14
IntroductionandSummary 121
1.5 CommunicationSignals 16
2.1 SineandCosine 122
1.6 PhysiologicSignals 21
2.2 Angles 123
1.7 ElectrocardiogramSignals 22
2.3 SeriesApproximations 124
1.8 ElectromyogramSignals 25
2.4 TrigonometricIdentities
1.9 Electroencephalogram andRelations 125
Signals 26
2.5 SinusoidalWaveforms 126
1.10 ElectrocorticogramSignals 28
2.6 SineorCosine? 128
1.11 NeuroelectricSignalsfrom
2.7 PeriodandFrequency 128
SingleNeurons 30
2.8 Phasors 129
1.12 Applicationsof
ElectrophysiologicSignals 32 2.9 LagandLead 129
1.13 Characterizationand 2.10 TimeShiftandPhaseShift 130
DecompositionofSignals 32
2.11 SummingPhasors 130
1.14 MathematicalRepresentations
2.12 CombinationofSinusoids 131
ofSignals 35
2.13 CombinationofPeriodic
1.15 TimeAverages 48
Signals 132
1.16 OperationsonSignals 51
2.14 RepresentationofaSum
1.17 TimeTransformation 51 ofSinusoids 132
1.18 EvenandOddFunctions 58 2.15 PowerinaSinusoid 133
1.19 IntegrationandSmoothing 61 2.16 One-SidedLineSpectrum 134
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viii Contents
2.17 ComplexRepresentation 3.16 Problems 188
ofSinusoidsandthe
3.17 Project:Open-LoopControl 200
Two-SidedSpectrum 136
2.18 Problems 137 Chapter 4
Superposition,Convolution,and
2.19 Project:Trajectories,Wave
Correlation 203
Polarization,andLissajous
Patterns 151 IntroductionandSummary 203
4.1 SuperpositionofResponses 204
Chapter 3
4.2 ConvolutionSum 211
Systems,Linearity,and
TimeInvariance 157 4.3 ConvolutionIntegral 214
IntroductionandSummary 157 4.4 GraphicalConvolution 217
3.1 FormulationofEquations 159 4.5 PropertiesofConvolution 222
3.2 ClassificationsofSystems 160 4.6 FilteringbyConvolution 226
3.3 Causality 162 4.7 MatchedFilter 228
3.4 Linearity,TimeInvariance, 4.8 Deconvolution 231
andLTISystems 162
4.9 Autocorrelation 233
3.5 DerivativeandIntegral
4.10 Cross-Correlation 237
PropertiesofLTISystems 166
4.11 CorrelationandConvolution 240
3.6 ExamplesfromElectric
Circuits 166 4.12 ConcludingRemarks 241
3.7 ExamplesfromOtherFields 172 4.13 Problems 242
3.8 ResponseofLTISystems 4.14 Project:SignalDetection
toImpulseandStepInputs 175 byMatchedFilter 255
3.9 ResponseofLTISystems
Chapter 5
toExponentialInputs 176
DifferentialEquationsandLTI
3.10 ResponseofLTISystems
Systems 259
toSinusoids 178
IntroductionandSummary 260
3.11 UseofSuperposition
andOtherProperties 5.1 FormulationofDifferential
ofLTISystems 179 Equations 260
3.12 LTISystemsandFourier 5.2 SolutionintheTimeDomain
Analysis 181 bytheClassicalMethod 270
3.13 AnalysisandSolutionMethods 5.3 TheParticularSolution 272
forLTISystems 182
5.4 TheHomogeneousSolution 274
3.14 ComplexSystems 183
5.5 ComposingtheComplete
3.15 NeuronalSystems 184 Solution 275
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Contents ix
5.6 ExamplesofComplete 6.2 LinearityProperty 317
Solutions 275
6.3 ExamplesoftheUnilateral
5.7 SpecialCase:Multiple LaplaceTransform 317
Roots 279
6.4 DifferentiationandIntegration
5.8 WhentheInputContains
Properties 320
NaturalFrequencies 280
6.5 Multiplicationbyt 323
5.9 WhentheNaturalResponse
MayBeAbsent 281 6.6 Multiplicationbyeat 324
5.10 ResponsetoanExponential 6.7 Time-ShiftProperty 324
Input 282
6.8 ScaleChange 325
5.11 TheSystemFunction 283
6.9 ConvolutionProperty 325
5.12 SinusoidalSteady-State
6.10 Initial-ValueandFinal-Value
Response 284
Theorems 327
5.13 Unit-StepResponse 285 6.11 LowerLimitofIntegration:
− +
0 ,0,0 328
5.14 Unit-ImpulseResponse 288
6.12 LaplaceTransformoftheUnit
5.15 EffectofDiscontinuityinthe
Impulse 328
ForcingFunction 290
6.13 TheInverseLaplace
5.16 SolutionbyConvolution 293
Transform 329
5.17 Zero-InputandZero-State
6.14 PartialFractionExpansion;
Responses 295
SimplePoles 331
5.18 Zero-StateResponseand
6.15 PartialFractionExpansion;
Convolution 298
Multiple-OrderPoles 335
5.19 PropertiesofLTIDifferential
6.16 SummaryoftheLaplace
Equations 299
TransformPropertiesand
5.20 SolutionbyNumerical Theorems 336
Methods 299
6.17 ATableofUnilateralLaplace
5.21 ConcludingRemarks 300 TransformPairs 337
5.22 Problems 301 6.18 CircuitSolution 338
5.23 Project:SystemofDifferential 6.19 SolutionofDynamical
Equations 310 Equations 340
6.20 BilateralLaplaceTransform 343
Chapter 6
6.21 RegionofConvergenceofthe
TheLaplaceTransformand
BilateralLaplaceTransform 346
ItsApplications 313
6.22 PropertiesoftheBilateralLaplace
IntroductionandSummary 314
Transform 348
6.1 DefinitionoftheLaplace
6.23 InverseoftheBilateralLaplace
Transform 315
Transform 349