数字信号处理英文版课后答案 (5)

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1、Chapter5Solutions5.1(a)x[n]=[n]+0.6065[n–1]+0.3679[n–2](b)Theonlynon-zerocomponentsinthesumarek=0,k=1andk=2.5.2Thesystem’sresponseto[n]ish[n],whiletheresponseto[n–1]ish[n–1].Therefore,whentheinputx[n]=[n]+[n–1]isappliedtothesystem,theoutputisy[n]=h[n]+h[n–1].

2、Thetwosignalsh[n]andh[n–1]canbesummedsamplebysample.5.5h[n]54.543.532.521.510.50-2024681012n5.5h[n–1]54.543.532.521.510.50-2024681012nh[n]+h[n–1]109876543210-2024681012n5.3(a)h[n–2]h[n–2]10.50-0.5-4-202468n(b)h[n+1]1h[n+1]0.50-0.5-4-202468n(c)h[–n]1h[–n]0.50-0.5-4-2

3、02468n(d)h[3–n]1h[3–n]0.50-0.5-4-202468n5.4Startingwithn=0,theinputx[n]hasthesamplevalues0,–1and–2.Startingwithn=0,theimpulseresponseh[n]hasthesamplevalues1,2,3and4.Thesesamplesareinsertedintoaconvolutiontable.Beyondn=5,alloutputsarezero.Thisisadirectresultofthefini

4、telengthsoftheinputandimpulseresponsesignals.x[k]0–1–2h[–k]4321y[0]=0h[1–k]4321y[1]=–1h[2–k]4321y[2]=–4h[3–k]4321y[3]=–7h[4–k]4321y[4]=–10h[5–k]4321y[5]=–8h[6–k]4321y[6]=05.5(a)x[k]1234567h[–k]1000y[0]=0h[1–k]1000y[1]=0h[2–k]1000y[2]=0h[3–k]1000y[3]=1h[4–k]1000y[4]=

5、2h[5–k]1000y[5]=3h[6–k]1000y[6]=4(b)Theimpulseresponseh[n]=[n–k]delaysthesignalbyksteps.5.6(a)Alloutputsamplesbeforen=0andaftern=8arezero.x[k]1111111h[–k]–0.2–0.41?y[0]=1.0h[1–k]–0.2–0.41?y[1]=0.6h[2–k]–0.2–0.41y[2]=0.4h[3–k]–0.2–0.41y[3]=0.4h[4–k]–0.2–0.41y[4]=0.4

6、h[5–k]–0.2–0.41y[5]=0.4h[6–k]–0.2–0.41y[6]=0.4h[7–k]–0.2–0.41?y[7]=–0.6h[8–k]–0.2–0.41?y[8]=–0.2(b)Theoutputsinfluencedbyboundaryeffectsareindicatedbyquestionmarks.5.7Theconvolutionoftheimpulseresponsewiththestepfunctionproducesthestepresponse.Thesamplesinthestepres

7、ponseare,ofcourse,cumulativesumsoftheimpulseresponsesamples.n0123456789h[n]1.0000.8500.7230.6140.5220.4440.3770.3210.2730.232s[n]1.0001.8502.5733.1873.7094.1524.5304.8505.1235.354n10111213141516171819h[n]0.1970.1670.1420.1210.1030.0870.0740.0630.0540.046s[n]5.5515.7

8、185.8615.9816.0846.1726.2466.3096.3636.408After17samples,thestepresponsesampleschangebylessthan1%.Thispointmaybeconsideredthebeginningofan