实验四线性时不变离散时间系统的频域分析综述.docx
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实验四线性时不变离散时间系统的频域分析综述.docx
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实验四线性时不变离散时间系统的频域分析综述
Name:
Chenyifan20112121006
Section:
LaboratoryExercise4
LINEAR,TIME-INVARIANTDISCRETE-TIMESYSTEMS:
FREQUENCY-DOMAINREPRESENTATIONS
4.1TRANSFERFUNCTIONANDFREQUENCYRESPONSE
Project4.1TransferFunctionAnalysis
Answers:
Q4.1ThemodifiedProgramP3_1tocomputeandplotthemagnitudeandphasespectraofamovingaveragefilterofEq.(2.13)for0ω2isshownbelow:
w=0:
pi/511:
2*pi;
M=input('M=');
num=ones(1,M)/M;
h=freqz(num,1,w);
subplot(2,1,1);
plot(w/pi,abs(h));grid;
title('H(e^{j\omega})幅度谱');
xlabel('\omega/\pi');ylabel('振幅');
subplot(2,1,2);
plot(w/pi,angle(h));grid;
title('相位谱H(e^{j\omega})');
xlabel('\omega/\pi');ylabel('以弧度为单位的相位');
ThisprogramwasrunforthefollowingthreedifferentvaluesofMandtheplotsofthecorrespondingfrequencyresponsesareshownbelow:
Thetypesofsymmetriesexhibitedbythemagnitudeandphasespectraaredueto-
Thetypeoffilterrepresentedbythemovingaveragefilteris
M=3
-
M=10;
M=20;
TheresultsofQuestionQ2.1cannowbeexplainedasfollows-Bythegraph,youcanseethatitrepresentsalow-passfilter.
Q4.2TheplotofthefrequencyresponseofthecausalLTIdiscrete-timesystemofQuestionQ4.2obtainedusingthemodifiedprogramisgivenbelow:
w=0:
pi/511:
pi;
num=[0.150-0.15];
den=[1-0.50.7];
h=freqz(num,den,w);
subplot(2,1,1);
plot(w/pi,abs(h));grid;
title('H(e^{j\omega})幅度谱');
xlabel('\omega/\pi');ylabel('振幅');
subplot(2,1,2);
plot(w/pi,angle(h));grid;
title('相位谱H(e^{j\omega})');
xlabel('\omega/\pi');
ylabel('以弧度为单位的相位');
Thetypeoffilterrepresentedbythistransferfunctionis-ItsaysbandpassfilterisobtainedbydiagramscanbeBPF
Q4.3TheplotofthefrequencyresponseofthecausalLTIdiscrete-timesystemofQuestionQ4.3obtainedusingthemodifiedprogramisgivenbelow:
w=0:
pi/511:
pi;
num=[0.150-0.15];
den=[0.7-0.51]
h=freqz(num,den,w);
subplot(2,1,1);
plot(w/pi,abs(h));grid;
title('H(e^{j\omega})幅度谱');
xlabel('\omega/\pi');ylabel('振幅');
subplot(2,1,2);
plot(w/pi,angle(h));grid;
title('相位谱H(e^{j\omega})');
xlabel('\omega/\pi');
ylabel('以弧度为单位的相位');
Thetypeoffilterrepresentedbythistransferfunctionis-Ocausallineartime-invariantdiscretetimesystemfrequencyresponse,determinethetypefilter
ThedifferencebetweenthetwofiltersofQuestions4.2and4.3is-Moreonthetopicoffigure,theamplitudespectrumisthesame,thephasespectrum,onthetopicthatiscontinuous,andkindsofphasejumpline,.
IshallchoosethefilterofQuestionQ4.3forthefollowingreason-theamplitudespectrumisthesame,thephasespectrum,onthetopicthatiscontinuous,andkindsofphasejumpline.
Q4.6Thepole-zeroplotsofthetwofiltersofQuestions4.2and4.3developedusingzplaneareshownbelow:
w=0:
pi/511:
pi;
num=[0.150-0.15];
den=[1-0.50.7];
h=zplane(num,den);
w=0:
pi/511:
pi;
num=[0.150-0.15];
den=[0.7-0.51];
h=zplane(num,den);
Fromtheseplotswemakethefollowingobservations:
Differentfunction,zerozeroandpolepolefigurewithdifferentrelativepositionofthecircle
4.2TYPESOFTRANSFERFUNCTIONS
Project4.2Filters
AcopyofProgramP4_1isgivenbelow:
clf;
fc=0.25;
n=[-6.5:
1:
6.5];
y=2*fc*sinc(2*fc*n);k=n+6.5;
stem(k,y);title('N=13');axis([013-0.20.6]);
xlabel('时间序号n');ylabel('振幅');grid
Answers:
Q4.7TheplotoftheimpulseresponseoftheapproximationtotheideallowpassfilterobtainedusingProgramP4_1isshownbelow:
clf;
fc=0.25;
n=[-6.5:
1:
6.5];
y=2*fc*sinc(2*fc*n);k=n+6.5;
stem(k,y);title('N=13');axis([013-0.20.6]);
xlabel('时间序号n');ylabel('振幅');grid
ThelengthoftheFIRlowpassfilteris-14
ThestatementinProgramP4_1determiningthefilterlengthis-n=[-6.5:
1:
6.5];
Theparametercontrollingthecutofffrequencyis-Fcparameterscontrolthecutofffrequency
Q4.8TherequiredmodificationstoProgramP4_1tocomputeandplottheimpulseresponseoftheFIRlowpassfilterofProject4.2withalengthof20andacutofffrequencyofωc=0.45areasindicatedbelow:
clf;
fc=0.45/(2*pi);
n=[-9.5:
1:
9.5];
y=2*fc*sinc(2*fc*n);k=n+9.5;
stem(k,y);title('N=20');axis([020-0.20.6]);
xlabel('时间序号n');ylabel('振幅');grid
Theplotgeneratedbyrunningthemodifiedprogramisgivenbelow:
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- 关 键 词:
- 实验 线性 不变 离散 时间 系统 分析 综述