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Conyolutionisatechniquefordeterminingtheoutputofa
Systeminresponsetoanygeneralinputwithoutleavingthe
TesponseTheimpulseresponseisusedasarepresentationof
thesystemsresponsetoaninfinitesimalsegmentoftheinput.
Ifthesystemislinearandsuperpositionholds,theimpulse
responseffomeachinputsegmentcanbesummedtoproduce
,
signalandtheimpulseresponse,Thisintegrationcanbe
cumbersomeforcomplicatedinputsignalsorimpulse
Tesponses,butieasytoprogram0nacomputer,Basic
MATLABprovidestworoutines,convandfltertoperform
convolutionTheconyroutineactuallyconyertstothe
ffequencydomain,multiplicsthetwosignals,thenconverts
backtothetimedomain,andisfsterthantheflterroutine,
Conyolutioniscommonlyused训signalprocessingto
implementdigitalfiltering,asissShowninChapter8.
Conyolutionrequiresknowledgeofthesystemsimpulse
canbedetermined,thentheimpulseresponsecanbeobtained
bytakingtheinverseoftheLaplacedomaintransferfunction
、IftheFouriertransformofthesystemis
known,theimpulseresponseisjusttheinverse
Fouriertransform,Finally,让thesystemexists,thenthe
impulsefunctioncanbedetermincddirectlybystimulating
thesystemwithanimpulse
Conyolutionperformsthesamefunctioninthetimedomain
a$
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true;convolution训theffequencydomainslike
multiplicationinthetimedomain,Thisctisusefulin
explainingcertaintimedomainoperationssuchaswindowing
andsampling.
Simulationisapowerfultimedomaintoolforexploringand
automaticallytimeslicingtheinputsignalanddctermining
theresponseofeachclementinturnuntilthefinaloutput
elementisreached、Thisanalysisisrepeatedtimesliceby
ofcachclementisanalyzedforeachtimeslice,itispossible
toexaminethebehaviorofanyclementaswellastheoverall
sSyst