1. Introduction to Signals and Systems .pdf

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1、1.IntroductiontoSignalsandSystems1.1.IntroductiontoSignals(1.1)1.2.IntroductiontoSystems(1.5)1.3.ClassificationofSystems(1.6)1.1.IntroductiontoSignalsAsignalisafunctionofoneormoreindependentvariables.Itcanbe,forexample,avoltageoranimage.Inourdiscussion,asignalisconsideredasafunctionoftime.H

2、owever,weshouldrealizethattheaddressedtheorymayalsoapplytoothercases.Acontinuous-timesignal,alsocalledananalogsignal,isdefinedalongacontinuumoftime.Anexampleofcontinuous-timesignalsisgiveninfigure1.1.x(t)=Aeat,t0toFigure1.1.AContinuous-TimeSignal.Adiscrete-timesignalisdefinedatdiscretetime

3、s.Figure1.2givesanexampleofdiscrete-timesignals.Adiscrete-timesignaliscalledadigitalsignalifitsamplitudeisquantizedtoaseriesofdiscretelevels.Anexampleofdigitalsignalsisgiveninfigure1.3.x(n)=Aan,n=0,1,2,…noFigure1.2.ADiscrete-TimeSignal.x(n)=round(Aan),n=0,1,2,…4321noFigure1.3.ADigitalSignal

4、.1.2.IntroductiontoSystemsAsystemisadevicewhichconvertsaninputsignalintoanoutputsignal.Theinputsignalisalsocalledexcitationandtheoutputsignalisalsocalledresponse.Acontinuous-timesystemisasystemwhoseinputandoutputarecontinuous-timesignals(figure1.4).Adiscrete-timesystemisasystemwhoseinputand

5、outputarediscrete-timesignals(figure1.5).Acontinuous-timesystemmaybeimplementedbyadiscrete-timesystem(figure1.6).Adiscrete-timesystemmaybeimplementedbyacontinuous-timesystem(figure1.7).x(t)y(t)=T[x(t)]y(t)Figure1.4.AContinuous-TimeSystem.x(n)y(n)=T[x(n)]y(n)Figure1.5.ADiscrete-TimeSystem.x

6、(n)y(n)x(t)C/Dy(n)=T[x(n)]D/Cy(t)Figure1.6.ImplementationofaContinuous-TimeSystembyaDiscrete-TimeSystem.x(t)y(t)x(n)D/Cy(t)=T[x(t)]C/Dy(n)Figure1.7.ImplementationofaDiscrete-TimeSystembyaContinuous-TimeSystem.1.3.ClassificationofSystems1.3.1.LinearSystemsversusNonlinearSystemsAsystem

7、islinearifitsatisfiesthefollowingcondition:Whentheinputisaweightedsumofseveralinputs,theoutputwillbetheweightedsumofthecorrespondingoutputs.Otherwise,thesystemisnonlinear.ForContinuous-TimeSystems:Letx1(t)andx2(t)betwoarbitrarysignals,andaandabetwoarbitr