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Linear systems and signals PDF

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“00-Lathi-Prelims” — 2017/9/28 — 9:43 — page i — #1 LINEAR SYSTEMS AND SIGNALS “00-Lathi-Prelims” — 2017/9/28 — 9:43 — page ii — #2 THE OXFORD SERIES IN ELECTRICAL AND COMPUTER ENGINEERING AdelS.Sedra,SeriesEditor AllenandHolberg,CMOSAnalogCircuitDesign,3rdedition Boncelet,Probability,Statistics,andRandomSignals Bobrow,ElementaryLinearCircuitAnalysis,2ndedition Bobrow,FundamentalsofElectricalEngineering,2ndedition Campbell,FabricationEngineeringattheMicro-andNanoscale,4thedition Chen,DigitalSignalProcessing Chen,LinearSystemTheoryandDesign,4thedition Chen,SignalsandSystems,3rdedition Comer,DigitalLogicandStateMachineDesign,3rdedition Comer,Microprocessor-BasedSystemDesign CooperandMcGillem,ProbabilisticMethodsofSignalandSystemAnalysis,3rdedition Dimitrijev,PrinciplesofSemiconductorDevice,2ndedition Dimitrijev,UnderstandingSemiconductorDevices Fortney,PrinciplesofElectronics:Analog&Digital Franco,ElectricCircuitsFundamentals Ghausi,ElectronicDevicesandCircuits:DiscreteandIntegrated GuruandHizirog˘lu,ElectricMachineryandTransformers,3rdedition Houts,SignalAnalysisinLinearSystems Jones,IntroductiontoOpticalFiberCommunicationSystems Krein,ElementsofPowerElectronics,2ndEdition Kuo,DigitalControlSystems,3rdedition LathiandGreen,LinearSystemsandSignals,3rdedition LathiandDing,ModernDigitalandAnalogCommunicationSystems,5thedition Lathi,SignalProcessingandLinearSystems Martin,DigitalIntegratedCircuitDesign Miner,LinesandElectromagneticFieldsforEngineers Mitra,SignalsandSystems Parhami,ComputerArchitecture Parhami,ComputerArithmetic,2ndedition RobertsandSedra,SPICE,2ndedition Roberts,Taenzler,andBurns,AnIntroductiontoMixed-SignalICTestandMeasurement,2ndedition Roulston,AnIntroductiontothePhysicsofSemiconductorDevices Sadiku,ElementsofElectromagnetics,7thedition Santina,Stubberud,andHostetter,DigitalControlSystemDesign,2ndedition Sarma,IntroductiontoElectricalEngineering Schaumann,Xiao,andVanValkenburg,DesignofAnalogFilters,3rdedition SchwarzandOldham,ElectricalEngineering:AnIntroduction,2ndedition SedraandSmith,MicroelectronicCircuits,7thedition Stefani,Shahian,Savant,andHostetter,DesignofFeedbackControlSystems,4thedition Tsividis,OperationandModelingoftheMOSTransistor,3rdedition VanValkenburg,AnalogFilterDesign WarnerandGrung,SemiconductorDeviceElectronics Wolovich,AutomaticControlSystems YarivandYeh,Photonics:OpticalElectronicsinModernCommunications,6thedition Z˙ak,SystemsandControl “00-Lathi-Prelims” — 2017/9/28 — 9:43 — page iii — #3 LINEAR SYSTEMS AND SIGNALS THIRD EDITION B. P. Lathi and R. A. Green NewYork Oxford OXFORDUNIVERSITYPRESS 2018 “00-Lathi-Prelims” — 2017/9/28 — 9:43 — page iv — #4 OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch, scholarship,andeducationbypublishingworldwide. Oxford NewYork Auckland CapeTown DaresSalaam HongKong Karachi KualaLumpur Madrid Melbourne MexicoCity Nairobi NewDelhi Shanghai Taipei Toronto Withofficesin Argentina Austria Brazil Chile CzechRepublic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore SouthKorea Switzerland Thailand Turkey Ukraine Vietnam Copyright(cid:2)c 2018byOxfordUniversityPress FortitlescoveredbySection112oftheUSHigherEducation OpportunityAct,pleasevisitwww.oup.com/us/heforthe latestinformationaboutpricingandalternateformats. PublishedbyOxfordUniversityPress. 198MadisonAvenue,NewYork,NY10016 http://www.oup.com OxfordisaregisteredtrademarkofOxfordUniversityPress. Allrightsreserved.Nopartofthispublicationmaybereproduced, storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans, electronic,mechanical,photocopying,recording,orotherwise, withoutthepriorpermissionofOxfordUniversityPress. LibraryofCongressCataloging-in-PublicationData Names:Lathi,B.P.(BhagwandasPannalal),author.| Green,R.A.(RogerA.),author. Title:Linearsystemsandsignals/B.P.LathiandR.A.Green. Description:ThirdEdition.|NewYork:OxfordUniversityPress,[2018]| Series:TheOxfordSeriesinElectricalandComputerEngineering Identifiers:LCCN2017034962|ISBN9780190200176(hardcover:acid-freepaper) Subjects:LCSH:Signalprocessing–Mathematics.|Systemanalysis.|Linear timeinvariantsystems.|Digitalfilters(Mathematics) Classification:LCCTK5102.5L2982017|DDC621.382/2–dc23LCrecord availableathttps://lccn.loc.gov/2017034962 ISBN978–0–19–020017–6 Printingnumber:9 8 7 6 5 4 3 2 1 PrintedbyR.R.DonnellyintheUnitedStatesofAmerica “00-Lathi-Prelims” — 2017/9/28 — 9:43 — page v — #5 C ONTENTS PREFACE xv B BACKGROUND B.1 ComplexNumbers 1 B.1-1 AHistoricalNote 1 B.1-2 AlgebraofComplexNumbers 5 B.2 Sinusoids 16 B.2-1 AdditionofSinusoids 18 B.2-2 SinusoidsinTermsofExponentials 20 B.3 SketchingSignals 20 B.3-1 MonotonicExponentials 20 B.3-2 TheExponentiallyVaryingSinusoid 22 B.4 Cramer’sRule 23 B.5 PartialFractionExpansion 25 B.5-1 MethodofClearingFractions 26 B.5-2 TheHeaviside“Cover-Up”Method 27 B.5-3 RepeatedFactorsofQ(x) 31 B.5-4 ACombinationofHeaviside“Cover-Up”andClearingFractions 32 B.5-5 ImproperF(x)withm=n 34 B.5-6 ModifiedPartialFractions 35 B.6 VectorsandMatrices 36 B.6-1 SomeDefinitionsandProperties 37 B.6-2 MatrixAlgebra 38 B.7 MATLAB:ElementaryOperations 42 B.7-1 MATLABOverview 42 B.7-2 CalculatorOperations 43 B.7-3 VectorOperations 45 B.7-4 SimplePlotting 46 B.7-5 Element-by-ElementOperations 48 B.7-6 MatrixOperations 49 B.7-7 PartialFractionExpansions 53 B.8 Appendix:UsefulMathematicalFormulas 54 B.8-1 SomeUsefulConstants 54 v “00-Lathi-Prelims” — 2017/9/28 — 9:43 — page vi — #6 vi Contents B.8-2 ComplexNumbers 54 B.8-3 Sums 54 B.8-4 TaylorandMaclaurinSeries 55 B.8-5 PowerSeries 55 B.8-6 TrigonometricIdentities 55 B.8-7 CommonDerivativeFormulas 56 B.8-8 IndefiniteIntegrals 57 B.8-9 L’Hôpital’sRule 58 B.8-10 SolutionofQuadraticandCubicEquations 58 References 58 Problems 59 1 SIGNALSAND SYSTEMS 1.1 SizeofaSignal 64 1.1-1 SignalEnergy 65 1.1-2 SignalPower 65 1.2 SomeUsefulSignalOperations 71 1.2-1 TimeShifting 71 1.2-2 TimeScaling 73 1.2-3 TimeReversal 76 1.2-4 CombinedOperations 77 1.3 ClassificationofSignals 78 1.3-1 Continuous-TimeandDiscrete-TimeSignals 78 1.3-2 AnalogandDigitalSignals 78 1.3-3 PeriodicandAperiodicSignals 79 1.3-4 EnergyandPowerSignals 82 1.3-5 DeterministicandRandomSignals 82 1.4 SomeUsefulSignalModels 82 1.4-1 TheUnitStepFunctionu(t) 83 1.4-2 TheUnitImpulseFunctionδ(t) 86 1.4-3 TheExponentialFunctionest 89 1.5 EvenandOddFunctions 92 1.5-1 SomePropertiesofEvenandOddFunctions 92 1.5-2 EvenandOddComponentsofaSignal 93 1.6 Systems 95 1.7 ClassificationofSystems 97 1.7-1 LinearandNonlinearSystems 97 1.7-2 Time-InvariantandTime-VaryingSystems 102 1.7-3 InstantaneousandDynamicSystems 103 1.7-4 CausalandNoncausalSystems 104 1.7-5 Continuous-TimeandDiscrete-TimeSystems 107 1.7-6 AnalogandDigitalSystems 109 1.7-7 InvertibleandNoninvertibleSystems 109 1.7-8 StableandUnstableSystems 110 “00-Lathi-Prelims” — 2017/9/28 — 9:43 — page vii — #7 Contents vii 1.8 SystemModel:Input–OutputDescription 111 1.8-1 ElectricalSystems 111 1.8-2 MechanicalSystems 114 1.8-3 ElectromechanicalSystems 118 1.9 InternalandExternalDescriptionsofaSystem 119 1.10 InternalDescription:TheState-SpaceDescription 121 1.11 MATLAB:WorkingwithFunctions 126 1.11-1 AnonymousFunctions 126 1.11-2 RelationalOperatorsandtheUnitStepFunction 128 1.11-3 VisualizingOperationsontheIndependentVariable 130 1.11-4 NumericalIntegrationandEstimatingSignalEnergy 131 1.12 Summary 133 References 135 Problems 136 2 TIME-DOMAINANALYSISOFCONTINUOUS-TIME SYSTEMS 2.1 Introduction 150 2.2 SystemResponsetoInternalConditions:TheZero-InputResponse 151 2.2-1 SomeInsightsintotheZero-InputBehaviorofaSystem 161 2.3 TheUnitImpulseResponseh(t) 163 2.4 SystemResponsetoExternalInput:TheZero-StateResponse 168 2.4-1 TheConvolutionIntegral 170 2.4-2 GraphicalUnderstandingofConvolutionOperation 178 2.4-3 InterconnectedSystems 190 2.4-4 AVerySpecialFunctionforLTICSystems: TheEverlastingExponentialest 193 2.4-5 TotalResponse 195 2.5 SystemStability 196 2.5-1 External(BIBO)Stability 196 2.5-2 Internal(Asymptotic)Stability 198 2.5-3 RelationshipBetweenBIBOandAsymptoticStability 199 2.6 IntuitiveInsightsintoSystemBehavior 203 2.6-1 DependenceofSystemBehavioronCharacteristicModes 203 2.6-2 ResponseTimeofaSystem:TheSystemTimeConstant 205 2.6-3 TimeConstantandRiseTimeofaSystem 206 2.6-4 TimeConstantandFiltering 207 2.6-5 TimeConstantandPulseDispersion(Spreading) 209 2.6-6 TimeConstantandRateofInformationTransmission 209 2.6-7 TheResonancePhenomenon 210 2.7 MATLAB:M-Files 212 2.7-1 ScriptM-Files 213 2.7-2 FunctionM-Files 214 “00-Lathi-Prelims” — 2017/9/28 — 9:43 — page viii — #8 viii Contents 2.7-3 For-Loops 215 2.7-4 GraphicalUnderstandingofConvolution 217 2.8 Appendix:DeterminingtheImpulseResponse 220 2.9 Summary 221 References 223 Problems 223 3 TIME-DOMAINANALYSISOFDISCRETE-TIMESYSTEMS 3.1 Introduction 237 3.1-1 SizeofaDiscrete-TimeSignal 238 3.2 UsefulSignalOperations 240 3.3 SomeUsefulDiscrete-TimeSignalModels 245 3.3-1 Discrete-TimeImpulseFunctionδ[n] 245 3.3-2 Discrete-TimeUnitStepFunctionu[n] 246 3.3-3 Discrete-TimeExponentialγn 247 3.3-4 Discrete-TimeSinusoidcos((cid:4)n+θ) 251 3.3-5 Discrete-TimeComplexExponentialej(cid:4)n 252 3.4 ExamplesofDiscrete-TimeSystems 253 3.4-1 ClassificationofDiscrete-TimeSystems 262 3.5 Discrete-TimeSystemEquations 265 3.5-1 Recursive(Iterative)SolutionofDifferenceEquation 266 3.6 SystemResponsetoInternalConditions:TheZero-InputResponse 270 3.7 TheUnitImpulseResponseh[n] 277 3.7-1 TheClosed-FormSolutionofh[n] 278 3.8 SystemResponsetoExternalInput:TheZero-StateResponse 280 3.8-1 GraphicalProcedurefortheConvolutionSum 288 3.8-2 InterconnectedSystems 294 3.8-3 TotalResponse 297 3.9 SystemStability 298 3.9-1 External(BIBO)Stability 298 3.9-2 Internal(Asymptotic)Stability 299 3.9-3 RelationshipBetweenBIBOandAsymptoticStability 301 3.10 IntuitiveInsightsintoSystemBehavior 305 3.11 MATLAB:Discrete-TimeSignalsandSystems 306 3.11-1 Discrete-TimeFunctionsandStemPlots 306 3.11-2 SystemResponsesThroughFiltering 308 3.11-3 ACustomFilterFunction 310 3.11-4 Discrete-TimeConvolution 311 3.12 Appendix:ImpulseResponseforaSpecialCase 313 3.13 Summary 313 Problems 314

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