实验四线性时不变离散时间系统的频域分析

实四性时变散系统频分析yifan20112121006Section

:LaboratoryLINEAR,TIME-INVARIANTDISCRETE-TIMEFREQUENCY-DOMAINREPRESENTATIONS4.1FUNCTIONANDFREQUENCYProject4.1TransferFunctionAnalysisAnswers:Q4.1ThemodifiedProgramP3_1tocomputeandplotthemagnitudeandphasespectraofamovingaveragefilterofEq.(2.13)for0

2isshownbelow

:<Insertprogramcodehere.Copyfromm-file(s)andpaste.>M=input('M=');plot(w/pi,abs(h));grid;幅度谱'振幅'title('相谱H(e^{j\omega})');以弧度为位的相'Thisprogramwasrunforthefollowingdifferentvaluesof:correspondingfrequencyresponsesareshownbelow

M

andtheplotsofthe<InsertMATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.>ThetypesofsymmetriesexhibitedbythemagnitudeandphasespectraduetoThetypeoffilterrepresentedbythemovingaveragefilteris

-M=3jjjjH(e)幅幅振

10.50

00.20.40.60.811.21.41.61.82位相的位单为度弧以-M=10;

420

H(e00.20.40.60.81

j)1.21.41.61.82H(e度谱幅振

10

00.20.61.4

相位谱H(e

)4位相的位单为度弧以

20-2-4

00.20.6

1.6jjM=20;H(e度谱幅振

10

00.20.61.4

相位谱H(e

)4位相的位单为度弧以

20-2-4

00.20.6

1.6TheresultsofQuestionQ2.1cannowbeexplainedasfollows

-

Bythegraph,youcanseethatitrepresentsalow-passfilter.Q4.2TheplotofthefrequencyresponseofthecausalLTIdiscrete-timesystemofQuestionQ4.2obtainedusingthemodifiedprogramisgivenbelow:w=0:pi/511:pi;

<InsertMATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.>0den=[1-0.5plot(w/pi,abs(h));grid;幅度谱'振幅'title('相谱H(e^{j\omega})');jj('\omega/\pi');('以弧为单位相位');H(e度谱幅振

10

00.10.3

相位谱H(e

)2位相的位单为度弧以

10-1-2

00.10.3

0.8Thetypeoffilterrepresentedbythistransferfunctionis

-

ItisbyQ4.3TheplotofthefrequencyresponseofthecausalLTIdiscrete-timesystemofQuestionQ4.3obtainedusingthemodifiedprogramisgivenbelow:w=0:pi/511:pi;

<InsertMATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.>0den=[0.7-0.5jjplot(w/pi,abs(h));grid;幅度谱'振幅'title('相谱H(e^{j\omega})');ylabel('以弧度为单位相位');)度谱幅振

0.5

0.10.20.40.60.7

H(e位相的位单为度弧以

0.10.20.4

0.6Thetypeoffilterrepresentedbythistransferfunctionis

-

OtimeThedifferencebetweenthetwofiltersofQuestions4.2and4.3is

-

ofisisof.IshallchoosethefilterofQuestionQ4.forthefollowingreason

-

isthetheof.Q4.6Thepole-zeroplotsofthetwofiltersofQuestions4.24.3developedusing

zplanearebeloww=0:pi/511:pi;0den=[1-0.5w=0:pi/511:pi;0den=[0.7-0.5

:<InsertMATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.>taritari1r0.2PyangamI

0-0.2-0.4-0.6-0.8-1-1-0.50RealPart

1trritrriaPyangamI

10-0.5-1-1.5-1-0.5RealPart

Fromthesemakethefollowingobservationspolefigurewithdifferentrelativepositionofthecircle4.2TYPESOFFUNCTIONSProject4.2Filters:AofProgramisgivenbelow

:

Differentfunction,zerozeroandpole

<Insertprogramcodehere.Copyfromm-file(s)andpaste.>k=n+6.5;title('N=13');axis([013xlabel('时间序号n');ylabel('振');grid--N=13幅振

0.60.50.40.30.20.10-0.1-0.2

0246时间序n

81012Answers:Q4.7TheplotoftheimpulseresponseoftheapproximationtotheideallowpassfilterobtainedusingProgramP4_1isshown:

<InsertMATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.>stem(k,y);title('N=13');axis([013-0.2xlabel('时间序号振'ThelengthoftheFIRlowpassfilteris

ThestatementinProgramP4_1determiningthefilterlengthis-TheparametercontrollingthecutofffrequencyisQ4.8TherequiredmodificationstoProgramP4_1tocomputeandplottheimpulseresponseoftheFIRfilterofProjectwithalengthof20andacutofffrequencyof

c

=

0.45

:areasindicatedbelow<Insertprogramcodehere.Copyfromm-file(s)andpaste.>stem(k,y);title('N=20');axis([020-0.2xlabel('时间序号n');ylabel('振'Theplotgeneratedbyrunningthemodifiedprogramisgivenbelow

:<InsertMATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.>幅振

0-0.1-0.2

01012时间序

14161820Q4.9TherequiredmodificationstoProgramP4_1tocomputeandplottheimpulseresponseoftheFIRfilterofProjectwithalengthof15andacutofffrequencyof

c

=0.65

areasindicatedbelow

:<Insertprogramcodehere.Copyfromm-file(s)andpaste.>stem(k,y);title('N=15');axis([014-0.2xlabel('时间序号n');ylabel('振'Theplotgeneratedbyrunningthemodifiedprogramisgivenbelow

:<InsertMATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.>幅振

0-0.1-0.2

0时间序

10Q4.11Aplotofthegainoflength-2movingaveragefilterobtainedusingP4_2isbelow:<InsertMATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.>unction--gain函数w=0:pi/255:pi;M=2;--滑动均低通波器的益响应序[g,w]=gain(num,1);plot(w/pi,g);grid;1-500.5])单位为b的增'',num2str(M)])0-5-10-15益-20增的-25bd为位单-35-40-45-50

200.10.3

0.8Fromtheplotitcanbeseenthatthe3-dBcutofffrequencyis

3dB。Q4.12TherequiredmodificationstoProgramtocomputeandplottheresponseofcascadeoflength-2movingaveragefiltersaregivenbelow<Insertprogramcodehere.Copyfromm-file(s)andpaste.>[g,w]=gainlink(num,den)\w=0:pi/255:pi;wc=2*acos(2^(-1/(2*3)))wcwc=0.3*piTheplotofthegainresponseforacascadeofsectionsobtainedusingthemodifiedprogramisshownbelow:<Insert

MATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.0-5-10-15益-20增的-25bd为位单-35-40-45-50

00.10.20.40.5

0.8>

Fromtheplotitcanbeseenthatthe3-dBcutofffrequencyofthecascadeis\wc=0.3*pi\

-Q4.19

AofProgramisgivenbelow

:<Insertprogramcodehere.Copyfromm-file(s)andpaste.>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('间序n');ylabel('振幅);grid;title('1型有限激响应滤');subplot(2,2,2);stem(n2,num2);xlabel('间序n');ylabel('振幅);grid;title('2型有限激响应滤');subplot(2,2,3);stem(n1,num3);xlabel('间序n');ylabel('振幅);grid;title('3型有限激响应滤');subplot(2,2,4);stem(n2,num4);xlabel('间序n');ylabel('振幅);grid;title('4型有限激响应滤');pausesubplot(2,2,1);zplane(num1,1);title('1型有限激响应滤');subplot(2,2,2);zplane(num2,1);title('2型有限激响应滤');subplot(2,2,3);zplane(num3,1);title('3型有限激响应滤');subplot(2,2,4);zplane(num4,1);title('4型有限激响应滤');disp('1型有冲激响应波器的零是');disp(roots(num1));disp('2型有冲激响应波器的零是');disp(roots(num2));disp('3型有冲激响应波器的零是');disp(roots(num3));disp('4型有冲激响应波器的零是');disp(roots(num4));TheplotsoftheimpulseresponsesoftheFIRfiltersgeneratedbyrunningProgramP4_3givenbelow:<InsertMATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.>型有冲激响滤器

型有激应滤波器

-50

-50

8

时间序号型有冲激响滤器

时间序型有激应滤波器

-50

-50

时间序号

时间序Fromtheplotsmakethefollowingobservations

:Filterisoflength

_____8_____

witha

___80_______

impulseresponseandisthereforeaType__linear-phaseFIRfilter

.Filter#2isoflength

____10______

witha

___80_______

impulseresponseandisthereforeaType

__

linear-phaseFIRfilter

.Filterisoflength

______8____

witha

___60_______

impulseresponseandisthereforeaType

__

linear-phaseFIRfilter

.Filter#4isoflength

______10____

witha

___80_______

impulseresponseandisthereforeaType__linear-phaseFIRfilter

.FromthezerosofthesefiltersgeneratedbyProgramobservethat

:Filter#1haszerosatz

=2.9744,2.0888,0.9790+-+-0.4784i,0.4787,0.3362Filter#2haszerosatz

=3.7585+-+-,0.0893-+-Filter#3haszerosatz

=4.7627,1.6279-,1.0000+0.2549i,0.1357-Filter#4haszerosatz

=,1.6541+-+--Plotsofthephaseofeachofthesefiltersobtainedusingareshownbelow<InsertMATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.>trritrritrritrritrritrritrritrri1有限冲激

2aPyangamI

10-1

8

aPyangamI

210-1-2

9-1

0

1

-2

0

2RealPart3有限冲激

RealPart4aPyangamI

20-2

8

aPyangamI

10-1

9-2

0

46

-102

3RealPartFromtheseconcludethateachofthesefiltershave

RealPart______linear____

phase

.Q4.20

TheplotsoftheimpulseresponsesoftheFIRfiltersgeneratedbyrunningProgramP4_3givenbelow:<InsertMATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.>1器100

2器50

50幅振

幅振000

2

468号n

0510n3器

4器幅振

1050-5

幅振

5000246号n

8

05n

10Fromtheplotsmakethefollowingobservations

:Filterisoflength

_____8_____

witha

___80_______

impulseresponseandisthereforeaType__linear-phaseFIRfilter

.Filter#2isoflength

____10______

witha

___80_______

impulseresponseandisthereforeaType

__

linear-phaseFIRfilter

.Filterisoflength

_____8_____

witha

_____5_____

impulseresponseandisthereforeaType

__

linear-phaseFIRfilter

.Filter#4isoflength

____10______

witha

____80______

impulseresponseandisthereforeaType

__

linear-phaseFIRfilter

.FromthezerosofthesefiltersgeneratedbyProgramobservethat

:Filter#1haszerosatz

=-+--0.2238+0.3559i,-0.2238-+-trritrritrritaaiamtrritrritrritaaiamFilter#2haszerosatz

=2.0392i,2.5270-2.0392i,-1.0101+-2.1930i,-1.0000,-0.1733+0.3762i,-0.1733-+-Filter#3haszerosatz

=,0.2602+1.2263i,0.2602-,0.6576+-+-Filter#4haszerosatz

=-+-,-0.2408-+-Plotsofthephaseofeachofthesefiltersobtainedusingareshownbelow<InsertMATLABfigure(s)here.Copyfromfigurewindow(s)andpaste.>1

22

2aPyangamI

10-1-2

8

aPyangamI

10-1-2

9aPyangam

10.50-0.5

-202-202RealPartRealPart2r1P89r0ng-1I

-1

I

-2-101-202RealPart

RealPartFromtheseconcludethateachofthesefiltershave

___linear_______phase.1212Answers:4.3STABILITYAofProgramisgivenbelow:<Insertprogramcodehere.Copyfromm-file(s)andpaste.>;=input(‘分母系=’);ki=poly2rc(den);disp(稳定性测试数’);disp(ki);Answers:Q4.23Thepole-zeroplotsofH(z)andH(z)obtained