数字信号处理_第二版或第一版_蔡宝坤_课后答案[1-10章]

1AppendixFAnswersToPartialProblemsAnswerstoPartialProblemsinChapter22.1012112312)(1n,nn,n,nynn.2.2101212)(1n,n,nyn.2.3.2212120)(2n,n,n,nxn;1211110)(1n,n,n,nxn.2.4(1)Periodic.200N;(2)Periodic.2N;(3)Periodic.14N;(4)Nonperiodic.2.8(1)For0nn,0)(ny;(2)For100Nnnn,)1()(011000,nn,nynnnnnn;(3)For10Nnn,)(001,N,nynnNNNnn.2.90n)1(1011)(,n,nyn.2.10(1)Unstable,causal,linear,time-invariantanddynamic;(2)Stable,causal,nonlinear,time-invariantandmemoryless;(3)Stable,causal,linear,time-varyingandmemoryless;(4)Unstable,causal,linear,time-varyinganddynamic;(5)Stableforbounded)(tg,causal,linear,time-varyingandmemoryless;(6)Stable.If00n,thenthesystemiscausal.Itislinearandtime-invariant.If00n,thesystemisdynamic;(7)Stable,causal,nonlinear,time-invariantandmemoryless.000))y((nnnn000021n,n,.1N,,(yy1NN22.11)5254()1()(jnynss.2.12)(418218)(nunynn.2.14(1))(312)()(nunnhn;(2))(31131121)(0001nue/e/enyjnjnj.AnswerstoPartialProblemsinChapter33.1(1)21)21()(/|z|,/zzzX;(2)21)21()(/|z|,/zzzX;(3)21/232213156275627625)(|z|,zzzzzzzX.3.2(1)1]1cos2[)sin()(20203|z|,zzzzzX;(2)r|z|,rzrzzrzAzXcos2)cos(cos)(20202.3.3(1)43:ROC1/|z|;431/2:ROC2/|z|;21:ROC3/|z|;(2)Threepossiblepole-zeroplotswithcorrespondingROCare,respectively,shownasfollows:FigureF3.3(3)For43/|z|,)(431312)(21134261Re2)(nunujjnxnn.44//;;(2)Threepossiblepole-zeroplotswithcorrespondingROCare,respectively,shown(2)Threepossiblepole-zeroplotswithcorrespondingROCare,respectively,shown2|z|||2r|z|,|zr|z|,|z)21/2:21/2|(2)Threepossiblepole-zeroplotswithcorrespondingROCare,respectively,shown(2)Threepossiblepole-zeroplotswithcorrespondingROCare,respectively,shown3For4321/|z|/,)1(431312)(21134261Re2)(nunujjnxnn.For21/|z|,)1(431312)1(21134261Re2)(nunujjnxnn3.4(1))1(417)(8)(nunnxn;(2))1(11)(1)(nuaaananxn;(3))1(2)(21)(nununxn.3.6(1))1(21)()(nunnxn;(2))1((2))(1nunxn;(3))(233612)(nunxnn;(4))(2131)1(2131)(2)2(nununxnn;(5))1(21)1()(1nunnxn.3.7(1))(4337)(34)(nunnhn;(2))(4313831138)(nunynn.3.9(1))()(jjeXeY;(2))()(jjeXeY;(3))()()(jjjeHeXeY;(4)deHeXeYjjj)()(21)()(;(5)dedXjeYjj)()(;(6))(21)(21)()2(2j/jjeXeXeY;(7))()(2jjeXeY;(8)deXeXeYjjj)()(21)()(.3.10(1)6)(0jeX;(2)2)(jeX;333311131388n())());)()u(;;313138n));;)((jj(((jj4(3)4)(deXj;(4)28|)(2deX|j;(5)316|)(2ddedX|j.3.1114sin22)(nnyss.3.12(1)251|2512511)(2|z,zzzzzzzH;(2)Thepole-zeroplotof)(zHwithitsROCisshownasfollows:FigureF3.10(3))(25151)(25151)(nununhnn;(4)Thesystemisunstable,becausetheROCdoesnotincludetheunitcircleinthez-plane.Ifwewanttoobtainastablesystem,theROCshouldbeselectedas251|251|z.Thecorrespondingimpulseresponseis)(25151)1(25151)(nununhnn.3.13(1)s.T0500,rad400;(2)n)020()280cos()(n.tn.txs;(3)Thesampledsequenceis)280cos()(n.nxanditsperiod5N.3.14(1)ROC:2|21|z/.Thecorrespondingimpulseresponse)(nhisatwo-sidedsequence;(2)Thereare2possibletwo-sidedimpulseresponseswhoseROCsare,respectively,givenby2|21|z/and3|2|z;22555(4)Thesystemisunstable,becausetheROCdoesnotincludetheunitcircleinthe(4)Thesystemisunstable,becausetheROCdoesnotincludetheunitcircleinthez-plane.Ifwewanttoobtainastablesystem,theROCshouldbeselectedasz-plane.Ifwewanttoobtainastablesystem,theROCshouldbeselectedasFigureF3.10FigureF3.10111)()(((4)Thesystemisunstable,becausetheROCdoesnotincludetheunitcircleinthe(4)Thesystemisunstable,becausetheROCdoesnotincludetheunitcircleinthez-plane.Ifwewanttoobtainastablesystem,theROCshouldbeselectedasz-plane.Ifwewanttoobtainastablesystem,theROCshouldbeselectedas1|||5(3)No,itisnotpossible.3.15(1)1|11)(|z,zzzH;(2)ROCy:1||z;(3))(2131)1(31)(nunynn.AnswerstoPartialProblemsinChapter44.1mNk,jmNk,mNk,jmNk,kX~3222212210)(,mintegeranyfor.4.2(1)Theperiodicsequenceisplottedasfollows:FigureF4.2(a)(2)Theprincipal-valuesequenceoftheDFS)(kX~is5255522363023610102361023635)(/j/j/j/je.e.e.e.kXThemagnitudeandphasesequencesare,respectively,plottedasfollows:FigureF4.2(b)FigureF4.2(c)Themagnitudeandphasesequencesare,respectively,plottedasfollows:Themagnitudeandphasesequencesare,respectively,plottedasfollows:(2)Theprincipal-valuesequenceoftheDFS(2)Theprincipal-valuesequenceoftheDFSXX(~~Themagnitudeandphasesequencesare,respectively,plottedasfollows:Themagnitudeandphasesequencesare,respectively,plottedasfollows:64.3(1))()(kRkXN;(2))()()(kRkNkXN;(3))()()2(0kRekXNN/jkn;(4))(11)(2kRekXNN/kjN;(5)2]2)1([002]2)1([0000)/2]2sin[()2sin()/2]2sin[()2sin()(/NkNj/NkNjeNk/NeNk/NkX;)10(Nk(6))()/2]2sin[()2sin()(2]2)1([000kReNk/NkXN/NkNj;(7)11102)1()(Nk,WNk,NNkXkN.4.4)()2cos()(0nRnkNnxN.4.5(1)Thesesequencesare,respectively,plottedasfollows:FigureF4.5(a)and(b)(2))()(1nxnxNN)())2(()(12nRnxnxNNNFigureF4.5(c)4.6(1)Omitted;4.5(1)Thesesequencesare,respectively,plottedasfollows:4.5(1)Thesesequencesare,respectively,plottedasfollows:7(2)130139148521340100,)()()(21nn,nn,nn,nnnxnxny;(3))()(1nxnyNN5311353113)(2nxN;(4)Becausethelengthofthecircularconvolutionsum)(nyNislessthanthelengthofthelinearconvolutionsum)(ny,)(nyNisnotequalto)(ny.However,ifweselectthelengthofthecircularconvolutionsumas14121NNN,then)(nyNisexactlyequalto)(ny.4.7(1)211)(/eeXjj;(2))(2110231024)(101nRnxn.4.8(1)Omitted;(2)Omitted.4.9(1))(11)](DFT[)(kRaWanxkXNk