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1、LabReportofDSP姚志浩5090309481F0903018Lab1Discrete-TimeFourierTransform(1Generateandplotthediscrete-timesignalSolution:It’sasimplesequence,wecangetthediscrete-timesignalusingMatlab.Chat1-1simplesequencesample(2DetermineandplottheDTFTofthesignalSolution:DTFTistheZ-TransformontheUnitCircle,wecaneasilyfi
2、ndtheZ-Transform：With‘freqz’function，wecangettheamplitude-frequencyandphasefrequencyresponsecurve.Chart1-2DTFTOfthesequence(3Alinearandtime-invariantsystemisdescribedbythedifferenceequationwhereabcdisequaltothelastfourdigitsofyourstudentIDnumber.(iIsthesystemBIBO-stable?(iiDetermineandsketchtheimpu
3、lseresponse,ofthesystem.Determinethestabilityofthesystembyobserving.(iiiDetermineandplottheoutputofthesystem,iftheinputis.Solution:(1MystudentIDnumberis5090309481，correspondingabcdwillbe9481,andthedifferenceequationwillbe；Characteristicequationwillbe，wecangetthreepolepoints:，Allthepolepointsareinth
4、eunitcircle,sothesystemisstable.(2Createafunction“impseq”togetaimpulsesignal.Hereweusethefunction“filter”,wecangettheimpulseresponse:Chart1-3UnitStepResponseWegetans=22.1234,sothesystemisstable.(3iftheinputis,theinputsequenceandoutputsequenceareshowed:Addendum：MatlabProgramList1-1.n=[0:30]x=(0.93.^
5、n.*cos(0.14*pi*n+pi/3;stem(n,x;title('x(n';xlabel('n';ylabel('x(n'1-2.n=[0:30];x=(0.89.^n.*(stepseq(0,30,0w=[0:500]*2*pi/500;X=exp(j*w./(exp(j*w-0.89*ones(1,501;mag=abs(X;ang=angle(Xfigure(1;plot(w/pi,mag;gridylabel('
6、X(w
7、';xlabel('w(inpiunit';title('DTFTofx(n-magnitude'figure(2;plot(w/pi,ang;gridy
8、label('argX(w/pi';xlabel('w(inpiunit';title('DTFTofx(n-angle'1-3.(2num=[9,-4,8,-1];den=[1,-0.65,0.35,0]x=impseq(0,0,100;n=[0:100]h=filter(num,den,xstem(n,h;xlabel('n';ylabel('y(n';title('ImpluseResponse';sum(abs(h(3num=[9,-4,8,-1];den=[1,-0.65,0.35,0]n=[0:200];x=(2+5*cos(0.27*pi*n+3*sin(0.77*pi*n.*
9、stepseq(0,200,0figure(1;stem(n,x;xlabel('n';ylabel('x(n';title('InputSequence';h=filter(num,den,x;figure(2;stem(n,h;xlabel('n';ylabel('y(n';title('OutputResponse'Functions:(1function[x,n]=impseq(n0,n1,n2n=[
