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1、Answerto“DigitalSignalProcessing”Problem1(a).x1(n)={3,7,-2,-1,5,-8},n1=-2:3x2(n)={3,7,-2,-1,5,-8},n2=1:6x3(n)={-8,5,-1,-2,7,3},n3=-2:3[3points](b)y(n)={14,9,-3,21,-11,-17,-5,-40,0},n=-2:6[3points](c).MATLABprogram:clear,closeall;n=0:5;x=[3,7,-2,-1,5,-8];[x1,n1]=sigshift(x,n,-2);[x2,n2]=sigshift(x,
2、n,1);[x3,n3]=sigfold(x,n);[x3,n3]=sigshift(x3,n3,3);[y1,yn1]=sigadd(2*x1,n1,x2,n2);[y1,yn1]=sigadd(y1,yn1,-x3,n3);[3points]stem(yn1,y1);title('sequenceY(n)’)Problem2(a)isperiodicinwithperiod2.[5points](b)Matlabprogram:clear;closeall;n=0:6;x=[4,3,2,0,2,3,4];w=[0:1:100]*pi/100;X=x*exp(-j*n'*w);magX=
3、abs(X);phaX=angle(X);%MagnitudeResponsePlotsubplot(2,1,1);plot(w/pi,magX);grid;xlabel('frequencyinpiunits');ylabel('
4、X
5、');title('MagnitudeResponse');%Phaseresponseplotsubplot(2,1,2);plot(w/pi,phaX*180/pi);grid;xlabel('frequencyinpiunits');ylabel('Degrees');title('PhaseResponse');axis([0,1,-180,180
6、])[5points](c)Becausethegivensequencex(n)={4,3,2,0,2,3,4}(n=0,1,2,3,4,5,6)issymmetricabout,thephaseresponsesatisfiedtheconditionsothephaseresponseisalinearfunctionin.[5points](d)[5points](e)Thedifferenceofamplitudeandmagnituderesponse:Firstly,theamplituderesponseisarealfunction,anditmaybebothposit
7、iveandnegative.Themagnituderesponseisalwayspositive.Secondly,thephaseresponseassociatedwiththemagnituderesponseisadiscontinuousfunction.Whiletheassociatedwiththeamplitudeisacontinuouslinearfunction.[5points]Problem3(a)Pole-zeroplot–MATLABscript:b=[1,1,0];a=[1,0.5,-0.24];zplane(b,a)Figure:Pole-zero
8、plotinProblemA2Becauseallthepolesandzeroareallintheunitcircle,sothesystemisstable.[5points](b)Differenceequationrepresentation.:;Aftercrossmultiplyingandinversetransforming;[5points](c)impulseresponsesequenceh(n)usingpartialfractionrepresentation:[5points](d)MATLABverification:(1)b=[1,1];a=[1,0.5,
9、-0.24];[delta,n]=impseq(0,0,9)x=filter(b,a,delta)(2)n=[0:4];x=(-0.1818.*(-0.8).^n+1.1818.*(0.3).^n).*stepseq(0,0,9)[5points]Problem4(a)figure4.1figure4.2sequencex1(n)sequencex2(n)Theplotsofx1(n)andx2(n)isshowninf
