2

Signals and Systems - Electrical Engineering

769 Pages · 2012 · 6.34 MB · English

  • Signals and Systems - Electrical Engineering

    Signals and Systems


    Using MATLAB


    Luis F. Chaparro


    Department of Electrical and Computer Engineering


    University of Pittsburgh


    AMSTERDAM•BOSTON•HEIDELBERG•LONDON


    NEWYORK•OXFORD•PARIS•SANDIEGO


    SANFRANCISCO•SINGAPORE•SYDNEY•TOKYO


    AcademicPressisanimprintofElsevier AcademicPressisanimprintofElsevier


    30CorporateDrive,Suite400,Burlington,MA01803,USA


    Elsevier,TheBoulevard,LangfordLane,Kidlington,Oxford,OX51GB,UK


    Copyright(cid:13)c 2011ElsevierInc.Allrightsreserved.


    Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicormechanical,


    includingphotocopying,recording,oranyinformationstorageandretrievalsystem,withoutpermissioninwritingfrom


    thepublisher.Detailsonhowtoseekpermission,furtherinformationaboutthePublisher’spermissionspoliciesandour


    arrangementswithorganizationssuchastheCopyrightClearanceCenterandtheCopyrightLicensingAgency,canbe


    foundatourwebsite:www.elsevier.com/permissions.


    ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher(otherthan


    (cid:13)


    asmaybenotedherein).MATLABR isatrademarkofTheMathWorks,Inc.andisusedwithpermission.TheMathWorks


    (cid:13)


    doesnotwarranttheaccuracyofthetextorexercisesinthisbook.ThisbooksuseordiscussionofMATLABR software


    orrelatedproductsdoesnotconstituteendorsementorsponsorshipbyTheMathWorksofaparticularpedagogical


    (cid:13)


    approachorparticularuseoftheMATLABR software.


    Notices


    Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperiencebroadenour


    understanding,changesinresearchmethods,professionalpractices,ormedicaltreatmentmaybecomenecessary.


    Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingandusingany


    information,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationormethodsthey


    shouldbemindfuloftheirownsafetyandthesafetyofothers,includingpartiesforwhomtheyhavea


    professionalresponsibility.


    Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeanyliability


    foranyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceorotherwise,


    orfromanyuseoroperationofanymethods,products,instructions,orideascontainedinthematerialherein.


    LibraryofCongressCataloging-in-PublicationData


    Chaparro,LuisF.


    (cid:13)


    SignalsandsystemsusingMATLABR/LuisF.Chaparro.


    p.cm.


    ISBN978-0-12-374716-7


    1.Signalprocessing–Digitaltechniques.2.Systemanalysis.3.MATLAB.I.Title.


    TK5102.9.C4722010


    621.382’2–dc22


    2010023436


    BritishLibraryCataloguing-in-PublicationData


    AcataloguerecordforthisbookisavailablefromtheBritishLibrary.


    ForinformationonallAcademicPresspublications


    visitourWebsiteatwww.elsevierdirect.com


    PrintedintheUnitedStatesofAmerica


    10 11 12 13 9 8 7 6 5 4 3 2 1 To my family, with much love. Contents


    PREFACE..................................................................................................................... xi


    ACKNOWLEDGMENTS................................................................................................ xvi


    Part 1 Introduction 1


    CHAPTER0 FromtheGroundUp!............................................................................. 3


    0.1 SignalsandSystemsandDigitalTechnologies........................................ 3


    0.2 ExamplesofSignalProcessingApplications........................................... 5


    0.2.1 Compact-DiscPlayer................................................................ 5


    0.2.2 Software-DefinedRadioandCognitiveRadio............................... 6


    0.2.3 Computer-ControlledSystems................................................... 8


    0.3 AnalogorDiscrete?............................................................................. 9


    0.3.1 Continuous-TimeandDiscrete-TimeRepresentations.................. 10


    0.3.2 DerivativesandFiniteDifferences ............................................. 12


    0.3.3 IntegralsandSummations......................................................... 13


    0.3.4 DifferentialandDifferenceEquations......................................... 16


    0.4 ComplexorReal?................................................................................ 20


    0.4.1 ComplexNumbersandVectors.................................................. 20


    0.4.2 FunctionsofaComplexVariable................................................ 23


    0.4.3 PhasorsandSinusoidalSteadyState.......................................... 24


    0.4.4 PhasorConnection................................................................... 26


    0.5 SoftIntroductiontoMATLAB ............................................................... 29


    0.5.1 NumericalComputations.......................................................... 30


    0.5.2 SymbolicComputations............................................................ 43


    Problems............................................................................................ 53


    Part 2 Theory and Application of Continuous-Time


    Signals and Systems 63


    CHAPTER1 Continuous-TimeSignals......................................................................... 65


    1.1 Introduction....................................................................................... 65


    1.2 ClassificationofTime-DependentSignals............................................... 66


    iv Contents v


    1.3 Continuous-TimeSignals..................................................................... 67


    1.3.1 BasicSignalOperations—TimeShiftingandReversal................... 71


    1.3.2 EvenandOddSignals.............................................................. 75


    1.3.3 PeriodicandAperiodicSignals.................................................. 77


    1.3.4 Finite-EnergyandFinitePowerSignals...................................... 79


    1.4 RepresentationUsingBasicSignals....................................................... 85


    1.4.1 ComplexExponentials.............................................................. 85


    1.4.2 Unit-Step,Unit-Impulse,andRampSignals................................. 88


    1.4.3 SpecialSignals—theSamplingSignalandtheSinc....................... 100


    1.4.4 BasicSignalOperations—TimeScaling,FrequencyShifting,


    andWindowing....................................................................... 102


    1.4.5 GenericRepresentationofSignals.............................................. 105


    1.5 WhatHaveWeAccomplished?WhereDoWeGofromHere?.................... 106


    Problems............................................................................................ 108


    CHAPTER2 Continuous-TimeSystems....................................................................... 117


    2.1 Introduction....................................................................................... 117


    2.2 SystemConcept.................................................................................. 118


    2.2.1 SystemClassification................................................................ 118


    2.3 LTIContinuous-TimeSystems.............................................................. 119


    2.3.1 Linearity................................................................................. 120


    2.3.2 TimeInvariance....................................................................... 125


    2.3.3 RepresentationofSystemsbyDifferentialEquations.................... 130


    2.3.4 ApplicationofSuperpositionandTimeInvariance ....................... 135


    2.3.5 ConvolutionIntegral................................................................. 136


    2.3.6 Causality................................................................................ 143


    2.3.7 GraphicalComputationofConvolutionIntegral........................... 145


    2.3.8 InterconnectionofSystems—BlockDiagrams.............................. 147


    2.3.9 Bounded-InputBounded-OutputStability................................... 153


    2.4 WhatHaveWeAccomplished?WhereDoWeGofromHere?.................... 156


    Problems............................................................................................ 157


    CHAPTER3 TheLaplaceTransform............................................................................ 165


    3.1 Introduction....................................................................................... 165


    3.2 TheTwo-SidedLaplaceTransform........................................................ 166


    3.2.1 EigenfunctionsofLTISystems................................................... 167


    3.2.2 PolesandZerosandRegionofConvergence ............................... 172


    3.3 TheOne-SidedLaplaceTransform........................................................ 176


    3.3.1 Linearity................................................................................. 185


    3.3.2 Differentiation......................................................................... 188


    3.3.3 Integration.............................................................................. 193


    3.3.4 TimeShifting........................................................................... 194


    3.3.5 ConvolutionIntegral................................................................. 196 vi Contents


    3.4 InverseLaplaceTransform................................................................... 197


    3.4.1 InverseofOne-SidedLaplaceTransforms................................... 197


    3.4.2 InverseofFunctionsContaininge−ρsTerms................................ 209


    3.4.3 InverseofTwo-SidedLaplaceTransforms................................... 212


    3.5 AnalysisofLTISystems....................................................................... 214


    3.5.1 LTISystemsRepresentedbyOrdinaryDifferentialEquations........ 214


    3.5.2 ComputationoftheConvolutionIntegral.................................... 221


    3.6 WhatHaveWeAccomplished?WhereDoWeGofromHere?.................... 226


    Problems............................................................................................ 226


    CHAPTER4 FrequencyAnalysis:TheFourierSeries.................................................. 237


    4.1 Introduction....................................................................................... 237


    4.2 EigenfunctionsRevisited..................................................................... 238


    4.3 ComplexExponentialFourierSeries...................................................... 245


    4.4 LineSpectra....................................................................................... 248


    4.4.1 Parseval’sTheorem—PowerDistributionoverFrequency............. 248


    4.4.2 SymmetryofLineSpectra......................................................... 250


    4.5 TrigonometricFourierSeries................................................................ 251


    4.6 FourierCoefficientsfromLaplace.......................................................... 255


    4.7 ConvergenceoftheFourierSeries......................................................... 265


    4.8 TimeandFrequencyShifting................................................................ 270


    4.9 ResponseofLTISystemstoPeriodicSignals........................................... 273


    4.9.1 SinusoidalSteadyState............................................................. 274


    4.9.2 FilteringofPeriodicSignals....................................................... 276


    4.10 OtherPropertiesoftheFourierSeries.................................................... 279


    4.10.1 ReflectionandEvenandOddPeriodicSignals............................. 279


    4.10.2 LinearityofFourierSeries—AdditionofPeriodicSignals............... 282


    4.10.3 MultiplicationofPeriodicSignals............................................... 284


    4.10.4 DerivativesandIntegralsofPeriodicSignals............................... 285


    4.11 WhatHaveWeAccomplished?WhereDoWeGofromHere?.................... 289


    Problems............................................................................................ 290


    CHAPTER5 FrequencyAnalysis:TheFourierTransform ........................................... 299


    5.1 Introduction....................................................................................... 299


    5.2 FromtheFourierSeriestotheFourierTransform.................................... 300


    5.3 ExistenceoftheFourierTransform....................................................... 302


    5.4 FourierTransformsfromtheLaplaceTransform..................................... 302


    5.5 Linearity,InverseProportionality,andDuality ........................................ 304


    5.5.1 Linearity................................................................................. 304


    5.5.2 InverseProportionalityofTimeandFrequency............................ 305


    5.5.3 Duality ................................................................................... 310 Contents vii


    5.6 SpectralRepresentation....................................................................... 313


    5.6.1 SignalModulation.................................................................... 313


    5.6.2 FourierTransformofPeriodicSignals......................................... 317


    5.6.3 Parseval’sEnergyConservation................................................. 320


    5.6.4 SymmetryofSpectralRepresentations........................................ 322


    5.7 ConvolutionandFiltering..................................................................... 327


    5.7.1 BasicsofFiltering.................................................................... 329


    5.7.2 IdealFilters............................................................................. 332


    5.7.3 FrequencyResponsefromPolesandZeros.................................. 337


    5.7.4 SpectrumAnalyzer................................................................... 341


    5.8 AdditionalProperties .......................................................................... 344


    5.8.1 TimeShifting .......................................................................... 344


    5.8.2 DifferentiationandIntegration.................................................. 346


    5.9 WhatHaveWeAccomplished?WhatIsNext? ....................................... 350


    Problems............................................................................................ 350


    CHAPTER6 ApplicationtoControlandCommunications ........................................... 359


    6.1 Introduction....................................................................................... 359


    6.2 SystemConnectionsandBlockDiagrams............................................... 360


    6.3 ApplicationtoClassicControl............................................................... 363


    6.3.1 StabilityandStabilization ......................................................... 369


    6.3.2 TransientAnalysisofFirst-andSecond-OrderControlSystems..... 371


    6.4 ApplicationtoCommunications............................................................ 377


    6.4.1 AMwithSuppressedCarrier..................................................... 379


    6.4.2 CommercialAM....................................................................... 380


    6.4.3 AMSingleSideband................................................................. 382


    6.4.4 QuadratureAMandFrequency-DivisionMultiplexing.................. 383


    6.4.5 AngleModulation.................................................................... 385


    6.5 AnalogFiltering.................................................................................. 390


    6.5.1 FilteringBasics........................................................................ 390


    6.5.2 ButterworthLow-PassFilterDesign........................................... 393


    6.5.3 ChebyshevLow-PassFilterDesign............................................ 396


    6.5.4 FrequencyTransformations ...................................................... 402


    6.5.5 FilterDesignwithMATLAB...................................................... 405


    6.6 WhatHaveWeAccomplished?WhatIsNext?........................................ 409


    Problems............................................................................................ 409


    Part 3 Theory and Application of Discrete-Time


    Signals and Systems 417


    CHAPTER7 SamplingTheory...................................................................................... 419


    7.1 Introduction....................................................................................... 419 viii Contents


    7.2 UniformSampling............................................................................... 420


    7.2.1 PulseAmplitudeModulation..................................................... 420


    7.2.2 IdealImpulseSampling ............................................................ 421


    7.2.3 ReconstructionoftheOriginalContinuous-TimeSignal................ 428


    7.2.4 SignalReconstructionfromSincInterpolation.............................. 432


    7.2.5 SamplingSimulationwithMATLAB........................................... 433


    7.3 TheNyquist-ShannonSamplingTheorem.............................................. 437


    7.3.1 SamplingofModulatedSignals.................................................. 438


    7.4 PracticalAspectsofSampling............................................................... 439


    7.4.1 Sample-and-HoldSampling....................................................... 439


    7.4.2 QuantizationandCoding.......................................................... 441


    7.4.3 Sampling,Quantizing,andCodingwithMATLAB........................ 444


    7.5 WhatHaveWeAccomplished?WhereDoWeGofromHere?.................... 446


    Problems............................................................................................ 447


    CHAPTER8 Discrete-TimeSignalsandSystems......................................................... 451


    8.1 Introduction..................................................................................... 451


    8.2 Discrete-TimeSignals.......................................................................... 452


    8.2.1 PeriodicandAperiodicSignals.................................................. 454


    8.2.2 Finite-EnergyandFinite-PowerDiscrete-TimeSignals................. 458


    8.2.3 EvenandOddSignals.............................................................. 461


    8.2.4 BasicDiscrete-TimeSignals...................................................... 465


    8.3 Discrete-TimeSystems........................................................................ 478


    8.3.1 RecursiveandNonrecursiveDiscrete-TimeSystems..................... 481


    8.3.2 Discrete-TimeSystemsRepresentedbyDifference


    Equations............................................................................... 486


    8.3.3 TheConvolutionSum............................................................... 487


    8.3.4 LinearandNonlinearFilteringwithMATLAB.............................. 494


    8.3.5 CausalityandStabilityofDiscrete-TimeSystems......................... 497


    8.4 WhatHaveWeAccomplished?WhereDoWeGofromHere?.................... 502


    Problems............................................................................................ 502


    CHAPTER9 TheZ-Transform...................................................................................... 511


    9.1 Introduction....................................................................................... 511


    9.2 LaplaceTransformofSampledSignals................................................... 512


    9.3 Two-SidedZ-Transform....................................................................... 515


    9.3.1 RegionofConvergence............................................................. 516


    9.4 One-SidedZ-Transform........................................................................ 521


    9.4.1 ComputingtheZ-TransformwithSymbolicMATLAB................... 522


    9.4.2 SignalBehaviorandPoles......................................................... 522


    9.4.3 ConvolutionSumandTransferFunction..................................... 526 Contents ix


    9.4.4 InterconnectionofDiscrete-TimeSystems................................... 537


    9.4.5 InitialandFinalValueProperties............................................... 539


    9.5 One-SidedZ-TransformInverse............................................................ 542


    9.5.1 Long-DivisionMethod.............................................................. 542


    9.5.2 PartialFractionExpansion........................................................ 544


    9.5.3 InverseZ-TransformwithMATLAB............................................ 547


    9.5.4 SolutionofDifferenceEquations................................................ 550


    9.5.5 InverseofTwo-SidedZ-Transforms............................................ 561


    9.6 WhatHaveWeAccomplished?WhereDoWeGofromHere?.................... 564


    Problems............................................................................................ 564


    CHAPTER10 FourierAnalysisofDiscrete-TimeSignalsandSystems........................... 571


    10.1 Introduction....................................................................................... 571


    10.2 Discrete-TimeFourierTransform.......................................................... 572


    10.2.1 Sampling,Z-Transform,Eigenfunctions,andtheDTFT................. 573


    10.2.2 DualityinTimeandFrequency.................................................. 575


    10.2.3 ComputationoftheDTFTUsingMATLAB .................................. 577


    10.2.4 TimeandFrequencySupports................................................... 580


    10.2.5 Parseval’sEnergyResult........................................................... 585


    10.2.6 TimeandFrequencyShifts........................................................ 587


    10.2.7 Symmetry............................................................................... 589


    10.2.8 ConvolutionSum ..................................................................... 595


    10.3 FourierSeriesofDiscrete-TimePeriodicSignals...................................... 596


    10.3.1 ComplexExponentialDiscreteFourierSeries.............................. 599


    10.3.2 ConnectionwiththeZ-Transform.............................................. 601


    10.3.3 DTFTofPeriodicSignals........................................................... 602


    10.3.4 ResponseofLTISystemstoPeriodicSignals ............................... 604


    10.3.5 CircularShiftingandPeriodicConvolution.................................. 607


    10.4 DiscreteFourierTransform .................................................................. 614


    10.4.1 DFTofPeriodicDiscrete-TimeSignals........................................ 614


    10.4.2 DFTofAperiodicDiscrete-TimeSignals...................................... 616


    10.4.3 ComputationoftheDFTviatheFFT .......................................... 617


    10.4.4 LinearandCircularConvolutionSums........................................ 622


    10.5 WhatHaveWeAccomplished?WhereDoWeGofromHere?.................... 628


    Problems............................................................................................ 629


    CHAPTER11 IntroductiontotheDesignofDiscreteFilters .......................................... 639


    11.1 Introduction....................................................................................... 639


    11.2 Frequency-SelectiveDiscreteFilters...................................................... 641


    11.2.1 LinearPhase........................................................................... 641


    11.2.2 IIRandFIRDiscreteFilters ....................................................... 643


    Please note: To fully download this free PDF,EBook files you need know All free.
    Found by internet command,site not saved pdf file
You May Also Like

Related PPT Template in the same category.