实验四线性时不变离散时间系统的频域分析Word下载.docx

实验四线性时不变离散时间系统的频域分析Word下载.docx

《实验四线性时不变离散时间系统的频域分析Word下载.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Word下载.docx（19页珍藏版）》请在冰豆网上搜索。

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））;

相位谱H（e^{j\omega}）'

以弧度为单位的相位'

ThisprogramwasrunforthefollowingthreedifferentvaluesofMandtheplotsofthecorrespondingfrequencyresponsesareshownbelow:

<

InsertMATLABfigure（s）here.Copyfromfigurewindow（s）andpaste.>

Thetypesofsymmetriesexhibitedbythemagnitudeandphasespectraaredueto-

Thetypeoffilterrepresentedbythemovingaveragefilteris

M=3

-

M=10;

M=20;

TheresultsofQuestionQ2.1cannowbeexplainedasfollows-Bythegraph,youcanseethatitrepresentsalow-passfilter.

Q4.2TheplotofthefrequencyresponseofthecausalLTIdiscrete-timesystemofQuestionQ4.2obtainedusingthemodifiedprogramisgivenbelow:

pi;

num=[0.150-0.15];

den=[1-0.50.7];

h=freqz（num,den,w）;

Thetypeoffilterrepresentedbythistransferfunctionis-ItsaysbandpassfilterisobtainedbydiagramscanbeBPF

Q4.3TheplotofthefrequencyresponseofthecausalLTIdiscrete-timesystemofQuestionQ4.3obtainedusingthemodifiedprogramisgivenbelow:

den=[0.7-0.51]

Thetypeoffilterrepresentedbythistransferfunctionis-Ocausallineartime-invariantdiscretetimesystemfrequencyresponse,determinethetypefilter

ThedifferencebetweenthetwofiltersofQuestions4.2and4.3is-Moreonthetopicoffigure,theamplitudespectrumisthesame,thephasespectrum,onthetopicthatiscontinuous,andkindsofphasejumpline,.

IshallchoosethefilterofQuestionQ4.3forthefollowingreason-theamplitudespectrumisthesame,thephasespectrum,onthetopicthatiscontinuous,andkindsofphasejumpline.

Q4.6Thepole-zeroplotsofthetwofiltersofQuestions4.2and4.3developedusingzplaneareshownbelow:

h=zplane（num,den）;

den=[0.7-0.51];

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]）;

时间序号n'

ylabel（'

grid

Q4.7TheplotoftheimpulseresponseoftheapproximationtotheideallowpassfilterobtainedusingProgramP4_1isshownbelow:

clf;

fc=0.25;

n=[-6.5:

y=2*fc*sinc（2*fc*n）;

k=n+6.5;

stem（k,y）;

axis（[013-0.20.6]）;

xlabel（'

grid

ThelengthoftheFIRlowpassfilteris-14

ThestatementinProgramP4_1determiningthefilterlengthis-n=[-6.5:

Theparametercontrollingthecutofffrequencyis-Fcparameterscontrolthecutofffrequency

Q4.8TherequiredmodificationstoProgramP4_1tocomputeandplottheimpulseresponseoftheFIRlowpassfilterofProject4.2withalengthof20andacutofffrequencyofωc=0.45areasindicatedbelow:

fc=0.45/（2*pi）;

n=[-9.5:

9.5];

k=n+9.5;

N=20'

axis（[020-0.20.6]）;

Theplotgeneratedbyrunningthemodifiedprogramisgivenbelow:

Q4.9TherequiredmodificationstoProgramP4_1tocomputeandplottheimpulseresponseoftheFIRlowpassfilterofProject4.2withalengthof15andacutofffrequencyofωc=0.65areasindicatedbelow:

fc=0.65/（2*pi）;

n=[-7.5:

k=n+7.5;

N=15'

axis（[014-0.20.6]）;

Q4.11Aplotofthegainresponseofalength-2movingaveragefilterobtainedusingProgramP4_2isshownbelow:

unction[g,w]=gain（num,den）--gain函数

pi/255:

g=20*log10（abs（h））;

M=2;

--滑动平均低通滤波器的增益响应程序

[g,w]=gain（num,1）;

plot（w/pi,g）;

axis（[01-500.5]）

单位为db的增益'

title（['

num2str（M）]）

Fromtheplotitcanbeseenthatthe3-dBcutofffrequencyisat-3dB。

Q4.12TherequiredmodificationstoProgramP4_2tocomputeandplotthegainresponseofacascadeofKlength-2movingaveragefiltersaregivenbelow:

function[g,w]=gainlink（num,den）\

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:

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）;

grid;

1型有限冲激响应滤波器'

subplot（2,2,2）;

stem（n2,num2）;

2型有限冲激响应滤波器'

subplot（2,2,3）;

stem（n1,num3）;

3型有限冲激响应滤波器'

subplot（2,2,4）;

stem（n2,num4）;

4型有限冲激响应滤波器'

pause

zplane（num1,1）;

zplane（num2,1）;

zplane（num3,1）;

zplane（num4,1）;

disp（'

1型有限冲激响应滤波器的零点是'

disp（roots（num1））;

2型有限冲激响应滤波器的零点是'

disp（roots（num2））;

3型有限冲激响应滤波器的零点是'

disp（roots（num3））;

4型有限冲激响应滤波器的零点是'

disp（roots（num4））;

TheplotsoftheimpulseresponsesofthefourFIRfiltersgeneratedbyrunningProgramP4_3aregivenbelow:

InsertMATLABfigure（s）here.Copyfromfigurewindow（s）andpaste.>

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:

Filter#2is