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Alinearsystem'scharacteristicsarecompletelyspecifiedbythesystem'simpulseresponse,asgovernedbythemathematicsofconvolution.Thisisthebasisofmanysignalprocessingtechniques.Forexample:Digitalfiltersarecreatedbydesigninganappropriateimpulseresponse.Enemyaircraftaredetectedwithradarbyanalyzingameasuredimpulseresponse.Echosuppressioninlongdistancetelephonecallsisaccomplishedbycreatinganimpulseresponsethatcounteractstheimpulseresponseofthereverberation.Thelistgoesonandon.Thischapterexpandsonthepropertiesandusageofconvolutioninseveralareas.First,severalcommonimpulseresponsesarediscussed.Second,methodsarepresentedfordealingwithcascadeandparallelcombinationsoflinearsystems.Third,thetechniqueofcorrelationisintroduced.Fourth,anastyproblemwithconvolutionisexamined,thecomputationtimecanbeunacceptablylongusingconventionalalgorithmsandcomputers.CHAPTERPropertiesofConvolution7Alinearsystem'scharacteristicsarecompletelyspecifiedbythesystem'simpulseresponse,asgovernedbythemathematicsofconvolution.Thisisthebasisofmanysignalprocessingtechniques.Forexample:Digitalfiltersarecreatedbydesigninganappropriateimpulseresponse.Enemyaircraftaredetectedwithradarbyanalyzingameasuredimpulseresponse.Echosuppressioninlongdistancetelephonecallsisaccomplishedbycreatinganimpulseresponsethatcounteractstheimpulseresponseofthereverberation.Thelistgoesonandon.Thischapterexpandsonthepropertiesandusageofconvolutioninseveralareas.First,severalcommonimpulseresponsesarediscussed.Second,methodsarepresentedfor……