实验四线性时不变离散时间系统的频域分析.docx
《实验四线性时不变离散时间系统的频域分析.docx》由会员分享，可在线阅读，更多相关《实验四线性时不变离散时间系统的频域分析.docx（19页珍藏版）》请在冰豆网上搜索。
实验四线性时不变离散时间系统的频域分析
实验四线性时不变离散时间系统的频域分析
Name:
Chenyifan20112121006
Section:
LaboratoryExercise4
LINEAR,TIME-INVARIANTDISCRETE-TIMESYSTEMS:
FREQUENCY-DOMAINREPRESENTATIONS
4.1TRANSFERFUNCTIONANDFREQUENCYRESPONSE
Project4.1TransferFunctionAnalysis
Answers:
Q4.1ThemodifiedProgramP3_1tocomputeandplotthemagnitudeandphasespectraofamovingaveragefilterofEq.（2.13）for0
ω
2πisshownbelow:
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:
Q4.9TherequiredmodificationstoProgramP4_1tocomputeandplottheimpulseresponseoftheFIRlowpassfilterofProject4.2withalengthof15andacutofffrequencyofωc=0.65areasindicatedbelow:
clf;
fc=0.65/（2*pi）;
n=[-7.5:
1:
6.5];
y=2*fc*sinc（2*fc*n）;k=n+7.5;
stem（k,y）;title（'N=15'）;axis（[014-0.20.6]）;
xlabel（'时间序号n'）;ylabel（'振幅'）;grid
Theplotgeneratedbyrunningthemodifiedprogramisgivenbelow:
Q4.11Aplotofthegainresponseofalength-2movingaveragefilterobtainedusingProgramP4_2isshownbelow:
unction[g,w]=gain（num,den）--gain函数
w=0:
pi/255:
pi;
h=freqz（num,den,w）;
g=20*log10（abs（h））;
M=2;--滑动平均低通滤波器的增益响应程序
num=ones（1,M）/M;
[g,w]=gain（num,1）;
plot（w/pi,g）;grid;
axis（[01-500.5]）
xlabel（'\omega/\pi'）;ylabel（'单位为db的增益'）;
title（['M=',num2str（M）]）
Fromtheplotitcanbeseenthatthe3-dBcutofffrequencyisat-3dB。
Q4.12TherequiredmodificationstoProgramP4_2tocomputeandplotthegainresponseofacascadeofKlength-2movingaveragefiltersaregivenbelow:
function[g,w]=gainlink（num,den）\
w=0:
pi/255:
pi;
h=freqz（num,den,w）;
H=h.*h.*h;
g=20*log10（abs（H））;
wc=2*acos（2^（-1/（2*3）））
wc=0.9430
wc=0.3*pi
Theplotofthegainresponseforacascadeof3sectionsobtainedusingthemodifiedprogramisshownbelow:
Fromtheplotitcanbeseenthatthe3-dBcutofffrequencyofthecascadeisat-
\wc=0.3*pi\
Q4.19AcopyofProgramP4_3isgivenbelow:
clf;
b=[1-8.530.5-63];
num1=[b81fliplr（b）];
num2=[b8181fliplr（b）];
num3=[b0-fliplr（b）];
num4=[b81-81-fliplr（b）];
n1=0:
length（num1）-1;
n2=0:
length（num2）-1;
subplot（2,2,1）;stem（n1,num1）;
xlabel（'时间序号n'）;ylabel（'振幅'）;grid;
title（'1型有限冲激响应滤波器'）;
subplot（2,2,2）;stem（n2,num2）;
xlabel（'时间序号n'）;ylabel（'振幅'）;grid;
title（'2型有限冲激响应滤波器'）;
subplot（2,2,3）;stem（n1,num3）;
xlabel（'时间序号n'）;ylabel（'振幅'）;grid;
title（'3型有限冲激响应滤波器'）;
subplot（2,2,4）;stem（n2,num4）;
xlabel（'时间序号n'）;ylabel（'振幅'）;grid;
title（'4型有限冲激响应滤波器'）;
pause
subplot（2,2,1）;zplane（num1,1）;
title（'1型有限冲激响应滤波器'）;
subplot（2,2,2）;zplane（num2,1）;
title（'2型有限冲激响应滤波器'）;
subplot（2,2,3）;zplane（num3,1）;
title（'3型有限冲激响应滤波器'）;
subplot（2,2,4）;zplane（num4,1）;
title（'4型有限冲激响应滤波器'）;
disp（'1型有限冲激响应滤波器的零点是'）;
disp（roots（num1））;
disp（'2型有限冲激响应滤波器的零点是'）;
disp（roots（num2））;
disp（'3型有限冲激响应滤波器的零点是'）;
disp（roots（num3））;
disp（'4型有限冲激响应滤波器的零点是'）;
disp（roots（num4））;
TheplotsoftheimpulseresponsesofthefourFIRfiltersgeneratedbyrunningProgramP4_3aregivenbelow:
Fromtheplotswemakethefollowingobservations:
Filter#1isoflength_____8_____witha___80_______impulseresponseandisthereforeaType__linear-phaseFIRfilter.
Filter#2isoflength____10______witha___80_______impulseresponseandisthereforeaType__linear-phaseFIRfilter.
Filter#3isoflength______8____witha___60_______impulseresponseandisthereforeaType__linear-phaseFIRfilter.
Filter#4isoflength______10____witha___80_______impulseresponseandisthereforeaType__linear-phaseFIRfilter.
FromthezerosofthesefiltersgeneratedbyProgramP4_3weobservethat:
Filter#1haszerosatz=2.9744,2.0888,0.9790+1.4110i,0.9790-1.4110i,0.3319+0.4784i,0.3319-0.4784i,0.4787,0.3362
Filter#2haszerosatz=3.7585+1.5147i,3.7585-1.5147i,0.6733+2.6623i,0.6733-2.6623i,-1.0000,0.0893+0.3530i,0.0893-0.3530i,0.2289+0.0922i,0.2289-0.0922i
Filter#3haszerosatz=4.7627,1.6279+3.0565i,1.6279-3.0565i,-1.0000,1.0000
0.1357+0.2549i,0.1357-0.2549i,0.2100
Filter#4haszerosatz=3.4139,1.6541+1.5813i,1.6541-1.5813i,-0.0733+0.9973i,-0.0733-0.9973i,1.0000,0.3159+0.3020i,0.3159-0.3020i,0.2929
PlotsofthephaseresponseofeachofthesefiltersobtainedusingMATLABareshownbelow:
Fromtheseplotsweconcludethateachofthesefiltershave______linear____phase.
Q4.20TheplotsoftheimpulseresponsesofthefourFIRfiltersgeneratedbyrunningProgramP4_3aregivenbelow:
Fromtheplotswemakethefollowingobservations:
Filter#1isoflength_____8_____witha___80_______impulseresponseandisthereforeaType__linear-phaseFIRfilter.
Filter#2is
升级会员 