《信号与系统》习题答案.doc

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1、Chapter1Problems1.1Sketchthewaveformoffollowingsignals.1．f（t）=(2-)u(t)2．f（t）=[u(t-1)-u(t-2)][u(t-1)-u(t-2)]3．f（t）=[u(t+1)-u(t-1)]4.f（t）=-78-1-2Writeouttheexpressionforallwareformasshownasbelow.1.f(t)=2.3.Letthen-78-SothatkT==1-3Determingwhetherthe1,cost,…,cosntareorthogonalfunctiononinterval

2、(0,2).Proof:=1.4Determingwhether1,x,,areorthogonalfunctionontheinterval[0.1].Proof:Sothatontheinterval[0.1]theyarenotorthogonal.1-5Findthevalueoftheintegral.1.2.34.5.-78-6.1-6Thewareformoff(t)isdepictedasbelow,pleasesketchthewaveformoff(t-3),f(-2t-1).Solution:f(t-3)f(-2t-1)1-7f(t)asshownasFi

3、g.Tryingtosketchthewaveformoffollowingsignals.-78-1.f(3t)2.f()u(3-t)3.4.1.8Plotthewareformofgivendiscretesignals.-78-1.2.3.4.5.-78-1-9Calculatetheconvolutionofand1.=u(t),=u(t)*====tu(t)2.=u(t),=*=====3.==4.,-78-====1-10Determingtheperiodicforthefollowingsignals.(1)Let===X(n)SotheperrodisN=40

4、(2)Let==SotheperiodisN=801-11Findthewaveformofthef1【(t)*f2(t)(a)Solution:f1(t)=u(t)–u(t-1),f2(t)=t[u(t)–u(t-2)]f1(t)*f2(t)=f2()f(t-)d=[u(z)-u(-2)][u(t-2)-u(t--1)]d={du(t)-du(t-1)-du(t-2)+-78-du(t-3)}=[u(t)-u(t-1)-(-2)u(t-2)]+[-2]u(t-3)OrcalculatebymeansofgraghWesee(1)0

5、d=-(t-z)2=t2(2)1

6、t0)f(t-t0)*(t-t0)=f(t-t0-t1)(c)Wefirstexpressthef1(t)andf2(t)byusingtheu(t)f(t)=u(t+∞)+u(t-1)f(t)=e-(t+1)u(t+1)Thenf1(t)*f2(t)=f()*f(t-)d=﹛u(+∞)-u(-1)﹜e-(t-z+1)u(t-+1)d=e-(t+1)｛ezdu(t+1+∞)+ezdu(t+1-1)｝=e-(t+1)｛et+1u(t+∞)+(et+1-e)u(t)｝=u(t+∞)+(1-e-t)u(t)-78-Chapter2Problems2-1.Theperiodicrect

7、angularsignalsasshownisFig2-1.FindtheFourierSerise(Triangularandexponentialform)andplottheamplitudeSpectrum.Solution:Letfo(t)denotefunctionthatistheoneperiodoffr(t).fo(t)isrepressedasFo(t)=--≤t<0Fo(t)=0≤t