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1、TestOfDigitalSignalProcessing1GivetheanswerofthefollowingproblemsaspossibleinEnglish.1 .Supposing一when”N.peasegiveitsZTX(z),DTFTX)andN-pointDFT“【Explaintherelationsamongthesethreetransfonns.1,O54n=2 .Areal8-pointsequence-0,6JIts8-pointDFTisXk.SUPPOSingy闵=MX内.SketchMm=5僧幻.(2)Determinethevalueofcos(),
2、012764,3. A sequencethe 128-point DFTXkLGiVe the expression of .O,otherwise4. AcausalLTIdiscrete-limesystemhasIhetransferfunction/(Z)=!(z-0.5)(z2-z+0.5)(1) Determinethedifferenceequationofthesystem.(2) Give(hepole-zeroplotandtheROCofthesystem.(3) Isthissystemstable?(4) Developarealizationofthesystem
3、inanycanonicform.5. DesignaFIRlinearphasecausalLPFwhichhascutofffrequency25,transjtonbandwidth口0.1万andminimumstopbandattenuation40d8.DeveloptheimpulseresponseinclosedIbrmbyWindowedFourierSeriesmethod.6.IfyouusefollowingMATLABprogramtodesignaIowpassfilter,whichhastheSpecificationszpassbandedge800Hz,s
4、topbandedgeIkHz,passbandripple0.5dB,minimunslopbandattenuation40dB,andsamplingrateis5kHz.Whatdatashouldyouinputtothecomputer?%ProgramForElIipticIIRLowpassFiIterDesign%Wp=input(Normalizedpassbandedge=)；Ws=input(Normalizedstopbandedge=,);Rp=input(PassbandrippleindB=);Rs=input(Minimumstopbandattenuatio
5、nindB=,);N,Wn=e11ipord(Wp,Ws,Rp,Rs)b,a=ellip(N,Wn);h.omega=freqz(b,a,256):plot(omega/pi,20*1og10(abs(h):grid;IabeI(omegapi,)；ylabel(Gain,dB,);title(,IIREllipticLowpassFiIter);7.InthesystemofFigure(a),hasabandlimitedspectrumassketchedinFigure(b)andisbeingsampledatH(ej)theNyquistrate.ThedigitalidealLP
6、FhasthefrequencyresponsezasshowninFigure(c).SketchthespectrumX()J()and 工。)of MM%nd 北 respectively.Figure(a)The DigitalProcessing of A Continuous Signal-2 oFigure (c)TestOfDigitalSignalProcessing2GivetheanswerofthefollowingproblemsinEnglishaspossibleasyoucan.f(n)=cos(-ri)+3sin(-ri)1. Determinethefund
7、amentalperiodofsequence32X(Z)3TT1-2(IdZT)(IzHz2)4482. Considerthez-transform(1) (1)Givethepole-zeroplotof().(2) (2)DetennineallpossibleROCsof.Discussthetypeofinversez-transform(left-sided,right-sided,ortwo-sidedsequences)associatedwitheachoftheseROCs.(3) (3)Givetheexpressionofright-sidedsequence.l,0
8、514n=0,673. Areal8-pointsequenceIJ.Its8-pointDFTisX伙.X0(1) Determinethevaluesof,=.Yk=WXkyn=IDFTYk(2) (2)Supposing.Sketchr4(3) (3)Determinethevalueofy = n*An4小瓦川=2W03andM网=W0 = 3 MY (N)式卜(2) (2)denotetheN-pointcircularconvolution.Determine%5thevaluesof,.Explainwhichvalueisequaltothe value of5Digital
9、Signal ProcessingsNote: Give the answer of the following problems as possible in English.xn= l,071 .(20 points J A length-8 sequence is given byQ. otherwiseX(Z).Please give its expressions of ZT2 . (20 points) Consider a length-8 real sequence, defined for hnPlease write a MATLAB program to computey
10、nbyFFT, plot the magnitude and phase spectrum ofy5.5,zA sequencehas DTFTH(ej)shown as following figure. SketchDTFTfilterisshownasfollowingfigure.ynY(ej)fyV= (-1),7z(h) f Hk= H(ejk)Yk = Y(ejk),whereSk=生 kk N4kWN-and *_* *.Give the expression betweenYk HkTestOfDigitalSignalProcessing4(GivetheanswerofthefollowingproblemsinEnglishaspossibleasyoucan)x1. 1.Asequenceisknownasbelow:Mh=A(1+j3)(3+jhA=(%,wherex(1) Sketchtherealpartof(2) IfA=I,isitperiodic?Ifitis,givei(speriod.2. 2.Foreachofthefollowingdiscrete-timesystems,whereynandxnare,respectively,theoutputandtheinputsequences,determinewhetheror
