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1、SOLUTIONSMANUALtoaccompanyDigitalSignalProcessing:AComputer-BasedApproachThirdEditionSanjitK.MitraPreparedbyChowdaryAdsumilli,JohnBerger,MarcoCarli,Hsin-HanHo,RajeevGandhi,ChinKayeKoh,LucaLucchese,andMyleneQueirozdeFariasNotforsale.1Chapter22.1(a)x11=22.85,x12=.91396,x1∞=.481,(b)x21=18.68,x22=.
2、71944,x2∞=.348.⎧,1n≥,0⎧,1n<,02.2µ[n]=⎨Hence,µ[−n−]1=⎨Thus,x[n]=µ[n]+µ[−n−1].⎩,0n<.0⎩,0n≥.0n2.3(a)Considerthesequencedefinedbyx[n]=∑δ[k.]Ifn<0,thenk=0isnotincludedk=−∞inthesumandhence,x[n]=0forn<0.Ontheotherhand,forn≥,0k=0isincludedinthesum,andasaresult,x[n]=1forn≥.0Therefore,n⎧,1n≥,0x[n]=∑δ[k]=
3、⎨=µ[n].⎩,0n<,0k=−∞⎧,1n≥,0⎧,1n≥,1(b)Sinceµ[n]=⎨itfollowsthatµ[n−]1=⎨Hence,⎩,0n<,0⎩,0n<.1⎧,1n=,0µ[n]−µ[n−]1=⎨=δ[n].⎩,0n≠,02.4Recallµ[n]−µ[n−]1=δ[n].Hence,x[n]=δ[n]+3δ[n−]1−2δ[n−]2+4δ[n−]3=(µ[n]−µ[n−1])+(3µ[n−]1−µ[n−2])−(2µ[n−]2−µ[n−3])+(4µ[n−]3−µ[n−4])=µ[n]+2µ[n−]1−5µ[n−]2+6µ[n−]3−4µ[n−4].2.5(a)c
4、[n]=x[−n+]2=2{0−3−215−4},↑(b)d[n]=y[−n−]3={−2780−1−3600},↑(c)e[n]=w[−n]=5{−20−122300},↑(d)u[n]=x[n]+y[n−]2={−451−23−31087−2},↑(e)v[n]=x[n]⋅w[n+]4=0{152−430−40},↑(f)s[n]=y[n]−w[n+]4={−34−500102−2},↑(g)r[n]=5.3y[n]={21−105.−5.308.2245.−7}.↑2.6(a)x[n]=−4δ[n+]3+5δ[n+]2+δ[n+]1−2δ[n]−3δ[n−]1+2δ[n−3],
5、y[n]=6δ[n+]1−3δ[n]−δ[n−]1+8δ[n−]3+7δ[n−]4−2δ[n−5],w[n]=3δ[n−]2+2δ[n−]3+2δ[n−]4−δ[n−]5−2δ[n−]7+5δ[n−8],(b)Recallδ[n]=µ[n]−µ[n−1].Hence,x[n]=−(4µ[n+]3−µ[n+2])+(5µ[n+]2−µ[n+1])+(µ[n+]1−µ[n])−(2µ[n]−µ[n−1])−(3µ[n−]1−µ[n−2])+(2µ[n−]3−µ[n−4])Notforsale.2=−4µ[n+]3+9µ[n+]2−4µ[n+]1−3µ[n]−µ[n−]1+3µ[n−]2+
6、2µ[n−]3−2µ[n−4],2.7(a)x[n-1]x[n-2]__x[n]z1z1h[0]h[1]h[2]++y[n]Fromtheabovefigureitfollowsthaty[n]=h]0[x[n]+h]1[x[n−]1+h]2[x[n−2].(b)h[0]w[n]x[n]++y[n]__z1z1β11β12x[n1]_+w[n1]_+__z1z1_β21β22x[n2]w[n2]_Fromtheabovefigurewegetw[n]=h0[](x[n]+β11x[n−]1+β21x[n−2])andy[n]=w[n]+β12w[n−]1+β22w[n−2].Maki
7、nguseofthefirstequationinthesecondwearriveaty[n]=h0[](x[n]+β11x[n−]1+β21x[n−2])+β12h0[](x[n−]1+β11x[n−]2+β21x[n−3])+β22h0[](x[n−]2+β11x[n−]3+β21x[n−4])=h]0[(x[n]+(β11+β12)x[n−]1+(β21+β12β11+β22)x[n−]2+(β12β21+β22β11)x[n−]3+β22β21x
