word文档信号与系统习题集

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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.)3()()2(ttuet().2.Theunitstepresponse)(tgisthezero-stateresponsewhentheinputsignalis().3.Giventwocontinuous–timesignalsx(t)andh(t),iftheirconvolutionisdenotedbyy(t),thentheconvolutionof)1(txand)1(this().4.Theconvolution)(*)(21ttttx().5.Theunitimpulseresponse)(thisthezero-stateresponsewhentheinputsignalis().6.Acontinuous–timeLTIsystemisstableifitsunitimpulseresponsesatisfiesthecondition:().7.Acontinuous–timeLTIsystemcanbecompletelydeterminedbyits().8.(t)dt2sin2tt().9.Giventwosequences}1,2,2,1{][nxand}5,6,3{][nh,theirconvolution][*][nhnx().10.GiventhreeLTIsystemsS1,S2andS3,theirunitimpulseresponsesare)(1th,)(2thand)(3threspectively.Now,constructanLTIsystemSusingthesethreesystems:S1parallelinterconnectedbyS2,thenseriesinterconnectedbyS3.theunitimpulseresponseofthesystemSis().11.Itisknownthatthezero-statresponseofasystemtotheinputsignalx(t)istdxty)()(,thentheunitimpulseresponseh(t)is().12.ThecompleteresponseofanLTIsystemcanbeexpressedasasumofitszero-stateresponseandits()response.13.ItisknownthattheunitstepresponseofanLTIsystemis)(2tuet,thentheunitimpulseresponseh(t)is().14.dtttttx))1()1((2sin)(0().15.Wecanbuildacontinuous-timeLTIsystemusingthefollowingthreebasicoperations:(),(),and().16.Thezero-stateresponseofanLTIsystemtotheinputsignal)1()()(tututxis)1()(tsts,wheres(t)istheunitstepresponseofthesystem,thentheunitimpulseresponse黄磊选择在线辅导,学科诊断+考题剖析广告掌门1对1在线辅导,精英教师测评,考点对症下药,逐个击破重难点查看详情>ish(t)=().17.Theblockdiagramofacontinuous-timeLTIsystemisillustratedinthefollowingfigure.Thedifferentialequationdescribingtheinput-outputrelationshipofthesystemis().18.Therelationshipbetweentheunitimpulseresponseh(t)andunitstepresponses(t)iss(t)=(),orh(t)=().二、选择题1.Foreachofthefollowingequations,()istrue.A、)()()1(tttB、)(2)1()1(tttC、)()()1(tdtttD、1)1()1(dttt2.Giventwocontinuous-timesignals)(txand)(th,iftheconvolutionof)(txand)(thisdenotedby)(ty,thentheconvolutionofsignals)1(txand)2(this().A.)(tyB.)1(tyC.)2(tyD.)1(ty3.TheunitimpulseresponseofanLTIsystemish(t)=te,thissystemis().A.causalandstableB.causalandunstableC.noncausalandunstableD.noncausalandstable4.dttttx)2()12()(112=().A.1B.3C.9D.05.ForanLTIsystem,iftheinputsignalis)(1tx,thecorrespondingoutputresponseis)(1ty,iftheinputsignalis)(2tx,thecorrespondingoutputresponseis)(2ty.Andiftheinputsignalis)()(21tbxtax,thecorrespondingoutputresponseis)()(21tbytay(aandbarearbitraryrealnumbers).Thenthesystemisa()system.A.linearB.causalC.nonlinearD.time–invariant6.)(*)(21ttttx=().)(tx+-)(ty+23重庆低压电工模拟考试题库广告安全生产模拟考试平台,免费提供主要负责人及安全管理人员,特种作业操作证,特种设备,查看详情>A.)(21tttxB.)(21tttxC.)(21tttxD.)(21ttt7.dtttttx6)sin()(().A.6B.16C.216D.2168.Giventwosequences][1nxand][2nx,theirlengthsareMandNrespectively.Thelengthoftheconvolutionof][1nxand][2nxis().A.MB.NC.NMD.1NM9.Theunitimpulseresponseofacontinuous-timeLTIsystemisdttdtth)()(2)(,thedifferentialequationdescribingtheinput-outputrelationofthissystemis().A.)()()(2txdttdytyB.)()(2)(txdttdytyC.dttdxtxty)()(2)(D.dttdxtxdttdy)(2)()(10.Theinput-outputrelationofacontinuous-timeLTIsystemisdescribedbythedifferentialequation:dttdxtxtydttdydttyd)()(2)(3)(2)(22.Theunitimpulseresponseofthesystemh(t)().A.doesnotinclude)(tB.includes)(tC.includesdttd)(D.isuncertain11.Signals)(1txand)(2txareshowninthefollowingfigures.Theexpressionoftheconvolution)(*)()(21txtxtxis().A.)1()1(tutuB.)2()2(tutuC.)1()1(tutuD.)2()2(tutu12.Thefollowingblockdiagramrepresentsacontinuous-timeLTIsystem.Theunitimpulse-1110-11(1)0)(1tx(1))(2tx高中数学搜题软件高考各科提分小技巧超级实用!广告亲身经历高中数学搜题软件高考超有效的提分方法,让你两个月达到理想成绩,查看详情>responseh(t)satisfies().A.)()()(txtydttdyB.)()()(tytxthC.)()()(tthdttdhD.)()()(tytth13.Theinput-outputrelationshipofacausalcontinuous-timesystemisdescribedbythedifferentialequation:dttdxtydttdy)(2)(3)(,thentheunitstepresponse)(ts().A.)(23tuetB.)(213tuetC.)(23tuetD.)(213tuet三、综合题(分析、计算题)1.Theinput-outputrelationshipofacontinuous-timeLTIsystemisdescribedbytheequation:dxetytt)2()()(,a.Determinetheunitimpulseresponseh(t)ofthesystem.b.Determinethesystemresponsey(t)totheinputsignal)2()1()(tututx.2.GivenanLTIsystemdepictedinFigure2.AssumethattheimpulseresponseoftheLTIsystemish(t)=e-tu(t),theinputsignalx(t)=u(t)-u(t-2).Determineandsketchtheoutputresponsey(t)ofthesystembyevaluatingtheconvolutiony(t)=x(t)*h(t).3.Rememberthefollowingidentities:)(*)()(ttxtx)(*)()(00tttxttx)()(*)(00tttttdttdhtxthdttdxdttdy)(*)()(*)()(4.ConsideranLTIsystemSandasignal)1(2)(3tuetxt.If)()(tytxand)()(3)(2tuetydttdxt,determinetheimpulseresponseh(t)ofS.)(tx)(ty)(thFigure2)(tx)(ty+-高中数学搜题软件推荐这几个提分技巧,高一高二高三都适用!广告高中数学搜题软件推荐2021年高考冲刺指南:最后100天掌握这几个复习技巧,快速提分!查看详情>5.Let)5()3()(tututxand)()(3tuetht,asillustratedintheFigure6.(a).Computey(t)=x(t)*h(t).(b).Computeg(t)=dx(t)/dt*h(t).(c).Howisg(t)relatedtoy(t)?6.Letktkttuety)3(*)()(ShowthattAety)(for0≤t<3,anddeterminethevalueA.7.AcausalLTIsystemisdescribedbythedifferentialequation:)()()(2)(3)(22txdttdxtydttdydttydIftheinputsignalis)()(2tuetxt,determinethezero-stateresponsey(t)ofthesystem.8.Inthisproblem,weillustrateoneofthemostimportantconsequencesofthepropertiesoflinearityandtimeinvariance.Specifically,onceweknowtheresponseofalinearsystemoralineartime-invariantsystemtoasingleinputorresponsestoseveralinputs,wecandirectlycomputetheresponsestomanyotherinputsignals.(a).ConsideranLTIsystemwhoseresponsetothesignalx1(t)inFigure9(a)isthesignaly1(t)illustratedinFigure9(b).Determineandsketchcarefullytheresponseofthesystemtotheinputx2(t)depictedinFigure9(c).(b).Determineandsketchtheresponseofthesystemconsideredinpart(a)totheinputx3(t)showninFigure9(d).)(txt5)(thtFigure6131t121)(2txt12141)(3txt12112t1214Figure9(a)(b)(c)2)(1ty(d))(1tx

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