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Solution Manual For Discrete-Time Signal Processing, 3rd Edition

Master your textbook problems with Solution Manual For Discrete-Time Signal Processing, 3rd Edition, providing comprehensive solutions and explanations.

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|"aqxd9/21/093:59AMPage1&Nw©2010byOppenheim.PublishedbyPearsonPrenticeHall,PearsonEducation,Inc.,UpperSaddleRiver,NJ.Allrightsreserved.Thismaterialisprotectedunderallcopyrightlawsastheycurrentlyexist.Noportionofthismaterialmaybereproduced,inanyformorbyanymeans,withoutpermissioninwritingfromthepublisher.2.1.(a)T(aln))=glnlaln]«Stable:Let|2[n]|<Mthen[T{z[n]|<|g[n]|M.So,itisstableif|g[n]|isbounded.«Causal:yin]=g[njzi[n]andyo[n]=gln]za[n],soifzy[n]=za[n]foralln<no,theny1[n]=2[n]foralln<no,andthesystemiscausal.©Linear:Tani[n]+bzafn])=gfnl(azan]+baafn]=ag[njai[n]+bg[njza[n]=aT(niln])+bT(zafn))Sothisislinear.oNottime-invariant:T(z[n—no])=glnjzn—no)# yln=no]=gln—noje(n—no]whichisnotTL*Memoryless:y[n]=T(z[n])dependsonlyonthen‘*valueofz,soitismemoryless.(b)T(zfn])=Xion,2lk]NotStable:|z[n]|<M=|T(z[n])|<Tj,|z[k]|<|n—no|M.Asn=co,T—oo,sonotstable.*NotCausal:T'(z[n])dependsonthefuturevaluesofzn]whenn<ny,sothisisnotcausal.®Linear:nT(azi[n)+baz)=)azi[k]+balk]k=nonn|=a}w]+b)mpm|>k=ngk=noTan=aT(z:[n])+bT(z2[n])Thesystemislinear.eNotTL:nT(zfnnol)=lknok=non-no=Yakk=0n—no#yn—nol=)alk]k=noThesystemisnotTIL.«NotMemoryless:Valuesofy[n]dependonpastvaluesforn>nq,sothisisnotmemoryless.(©)T(zln))RIN,zlK]oStable:[T(zfnl)]<Tm,2{k]]<Site,2lklM<[2no+1Mfor[ala]<M,soitisstable.«NotCausal:T'(z[r])dependsonfuturevaluesofz[n],soitisnotcausal.eoLinear:ntnoT(azy[n]+bz2[n])=>az[k]+bza[k]k=n—non+ngning=aYall+bYz[k=aT(zi[n])+bT(z2[n])k=n—nok=n-no(+1&Nw

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