信号与系统练习题集第一部分：信号与系统的时域分析一、填空题1.().2.Theunitstepresponseisthezero-stateresponsewhentheinputsignalis().3.Giventwocontinuous–timesignalsx(t)andh(t),iftheirconvolutionisdenotedbyy(t),thentheconvolutionofandis().4.Theconvolution().5.Theunitimpulseresponseisthezero-stateresponsewhentheinputsignalis().6.Acontinuous–timeLTIsystemisstableifitsunitimpulseresponsesatisfiesthecondition:().7.Acontinuous–timeLTIsystemcanbecompletelydeterminedbyits().8.().9.Giventwosequencesand,theirconvolution().10.GiventhreeLTIsystemsS1,S2andS3,theirunitimpulseresponsesare,andrespectively.Now,constructanLTIsystemSusingthesethreesystems:S1parallelinterconnectedbyS2,thenseriesinterconnectedbyS3.theunitimpulseresponseofthesystemSis().11.Itisknownthatthezero-statresponseofasystemtotheinputsignalx(t)is,thentheunitimpulseresponseh(t)is().12.ThecompleteresponseofanLTIsystemcanbeexpressedasasumofitszero-stateresponseandits()response.13.ItisknownthattheunitstepresponseofanLTIsystemis,thentheunitimpulseresponseh(t)is().14.().15.Wecanbuildacontinuous-timeLTIsystemusingthefollowingthreebasicoperations:(),(),and().16.Thezero-stateresponseofanLTIsystemtotheinputsignalis,wheres(t)istheunitstepresponseofthesystem,thentheunitimpulseresponseish(t)=().17.Theblockdiagramofacontinuous-timeLTIsystemisillustratedinthefollowingfigure.Thedifferentialequationdescribingtheinput-outputrelationshipofthesystemis().18.Therelationshipbetweentheunitimpulseresponseh(t)andunitstepresponses(t)iss(t)=(),orh(t)=().二、选择题1.Foreachofthefollowingequations,()istrue.A、B、C、D、2.Giventwocontinuous-timesignalsand,iftheconvolutionofandisdenotedby,thentheconvolutionofsignalsandis().A.B.C.D.3.TheunitimpulseresponseofanLTIsystemish(t)=,thissystemis().A.causalandstableB.causalandunstableC.noncausalandunstableD.noncausalandstable4.=().A.1B.3C.9D.05.ForanLTIsystem,iftheinputsignalis,thecorrespondingoutputresponseis,iftheinputsignalis,thecorrespondingoutputresponseis.Andiftheinputsignalis,thecorrespondingoutputresponseis(aandbarearbitraryrealnumbers).Thenthesystemisa()system.A.linearB.causalC.nonlinearD.time–invariant6.=().A.B.C.D.7.().A.B.C.D.)(tx+--)(ty+238.Giventwosequencesand,theirlengthsareMandNrespectively.Thelengthoftheconvolutionofandis().A．B．C．D．9.Theunitimpulseresponseofacontinuous-timeLTIsystemis,thedifferentialequationdescribingtheinput-outputrelationofthissystemis().A.B.C.D.10.Theinput-outputrelationofacontinuous-timeLTIsystemisdescribedbythedifferentialequation:.Theunitimpulseresponseofthesystemh(t)().A.doesnotincludeB.includesC.includesD.isuncertain11.Signalsandareshowninthefollowingfigures.Theexpressionoftheconvolutionis().A.B.C.D.12.Thefollowingblockdiagramrepresentsacontinuous-timeLTIsystem.Theunitimpulseresponseh(t)satisfies().A.B.C.D.13.Theinput-outputrelationshipofacausalcontinuous-timesystemisdescribedbythedifferentialequation:-1110-11(1)0)(1tx(1))(2tx)(tx)(ty+--,thentheunitstepresponse().A.B.C.D.三、综合题（分析、计算题）1.Theinput-outputrelationshipofacontinuous-timeLTIsystemisdescribedbytheequation:，a.Determinetheunitimpulseresponseh(t)ofthesystem.b.Determinethesystemresponsey(t)totheinputsignal.2.GivenanLTIsystemdepictedinFigure2.AssumethattheimpulseresponseoftheLTIsystemish(t)=e-tu(t),theinputsignalx(t)=u(t)-u(t-2).Determineandsketchtheoutputresponsey(t)ofthesystembyevalu...
