资源描述：
《英文版数字信号处理去年考试题》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
1、1・ConsideranLTIsystemwithinputx[n]andoutputy[n]thatsatisfiesthedifferenceequation311y[n]+-y[n-1]+-y[n-2]=x[n]--x[n-l]482a.FindthesystemfunctionH(z).HowmanyROCsareassociatedwithH(z)?Foreachcase,determinewhattypeofthecorrespondingimpulseresponsehfnl?b・Ifthissystemiscausal,th
2、enisitstable?Justifyyouranswer.AndwhetherH(eyh)existsornot?Ifitexists,determineH(eJW).2>Considcrthefinite-lengthsequencex[n]={l,0,2,l},0WnW3,withan4-pointDFTgivenbyx[kj.a.Ifthe4-pointDFTy[k]oflength-4sequencey[n]isgivenbyy(k)=x[k]、determiney[n].b.Ifthe4-pointDFTw[kjoflengt
3、h-4sequencew[n]isdenotedbyw(k)=xIk],determinew[n].c.IfN・pointDFTsareusedinthetwo-stepprocedure,howshouldwechooseNsothatw[n]=x[n]*x[n]for0=n=N-l?Determinew[n]inthecasealso.Note:usingtheDFTpropertieswithoutcomputingx[k]・3.Givenx[n]={0,l,2,3,4,5,6}bealength-7sequencedefinedfo
4、r0三nw6,withX(£八)denotingitsDTFTa)Evaluatethefollowingfunctionwithoutcomputingthetransformitself:X(R°)；『
5、兀(严)
6、2血；J-/T・2/rj—kb)DefineY[kJ=X(e5),0=n=4,withy[n]denotingits5-pointIDFT.Determiney[n]withoutcomputingY[k]anditsIDFT.CanyourecoverX[n]fromyfn].4.AnHRfilterisdescribedb
7、ythefollowingsystemfunction:0.44z2+0.36z+0.020.44z2+0.362z+0.02H(z)==一z'+0.4z+0.18z—0.2(z~+0.8z+0・5)(z—0.4)Determineanddrawthefollowingstructures:(a)DirectfromII(b)Cascadeform.3.VerifytheidentityequationN-=0Nf°rk~'=rN0otherwiseisamnteger3.Acontinuous-timesignalXa([}=cos(
8、27Tx300t)+(27Tx500t)+(2^x12000issampledata2kHzrate,andthesampledsequenceispassedthroughanideallovvpassfilterwithacutofffrequencyof900Hz,generatingacontinuous-timesignalya(l).a.Determinethediscrete-timesignalxfn]generatedbyperiodicallysamplingXu(z)atFr=2khzb.Whatarethefrequ
9、encycompontspresentinthereconstructedsignalya{{).c.Ifya(l)isequaltotheoriginalcontinuoussignal^determinethesamplingfrequencyinthiscased.Ifwewanttopassthefrequencycomponentsat300Hz,whattypefilterweshouldchoose?Ifthetransition-widthisassumedtoas100Hz,theminimumstopandattenua
10、tion(Xs=52dB、whichwindowfunctionscanwechoosefromTable1?Determinethelengthofthefilterforth
