信号与系统-半期试卷

SIGNALSANDSYSTEMS一．(60points).Eachofthefollowingquestionsmayhaveoneortworightanswers,justifyyouranswersandwriteitintheblank.1.（）（a) (b) (c) (d) 02.Iftheconvolutionintegral,thesignalx(t)mustbe()(a)(b)1(c)(d)3.ConsideranLTIsystemwhoseunitimpulseresponseh[n]aregivenby.Theoutputy[n]=x[n]*h[n]ofthissystemis()(a)x[n] (b)x[n-1](c)x[n+1] (d)ax[n+1]4.ConsideranLTIsystemwithinputandoutputthroughtheequation.Whatistheimpulseh(t)forthissystem()(a)h(t)=cos(t+1)u(t+1)(b)h(t)=cos(t)u(t)(c)h(t)=cos(t-1)u(t-1)(d)h(t)=cos(t+1)5.Thefundamentalperiodofthesignalis（）（a）(b)(c)(d)6.Whichofthefollowingsystemsisanlinearsystem()(a)(b)(c)(d)7.Whichofthefollowingsystemsisnotastablesystem()(a)(b)(c)(d)8.Letand.TheFourierseriescoefficientsofx(t)maybe()(a)and(b)and(c)and(d)and9.Consideracontinuous-timeLTIsystemwhosefrequencyresponseis.Ifweinputaperiodicoddsignaltothissystem,andgettheoutputy(t)=0,thentheperiodoftheinputsignalmaybe()(a)T=1(b)T=2(c)T=0.5(d)T=310.WhichofthefollowingLTIsystemsarecausalandstablesystem().Ineachexample,h[n]denotestheimpulseresponseofthefollowingsystems.(a)(b)(c)(d)2.（10分）Acontinuous-timesignalx(-3t+2)isillustratedinfigure2.(a)Determinethesignalx(t).(b)Sketchandlabelcarefullyx(t).Figure13.(15分）ConsideranLTIsystemwhoseresponsetothesignalx1(t)infigure2isthesignaly1(t)illustratedinFigure3.Determinetheresponsey2(t)totheinputsignalx2(t)depictedinfigure4.Figure2figure3figure44.(15points)Consideracontinuous-timeLTIsystemwhosefrequencyresponseH(jw)isillustratedinfigure5.Iftheinputsignal,determinetheoutputy(t)ofthissystem.