西安电子科技大学数字信号处理上机作业资料Word格式.docx
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西安电子科技大学数字信号处理上机作业资料Word格式.docx
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n'
subplot(2,1,2)
stem(t,y);
3.结果
4.结果分析
M2.4
(a)Writeamatlabprogramtogenerateasinusoidalsequencex[n]=Acos(ω0n+Ф)andplotthesequenceusingthestemfunction.TheinputdataspecifiedbytheuserarethedesiredlengthL,amplitudeA,theangularfrequencyω0,andthephaseФwhere0<
ω0<
piand0<
=Ф<
=2pi.Usingthisprogramgeneratethesinusoidalsequencesshowninfigure2.15.
(b)GeneratesinusoidalsequenceswiththeangularfrequenciesgiveninProblem2.22.Determinetheperiodofeachsequencefromtheplotandverifytheresulttheoretically.
%用户定义的参数
Desiredlength='
Amplitude='
omega=input('
Angularfrequency='
phi=input('
Phase='
%信号产生
n=0:
x=A*cos(omega*n+phi);
stem(n,x);
title(['
\omega_{o}='
num2str(omega)]);
(a)
ω0=0
ω0=0.1π
ω0=0.8π
ω0=1.2π
(b)
ω0=0.14π
ω0=0.24π
ω0=0.34π
ω0=0.68π
ω0=0.75π
M2.5
Generatethesequencesofproblem2.21(b)to2.21(e)usingmatlab.
n=0:
99;
x=sin(0.6*pi*n+0.6*pi);
(c)
x=2*cos(1.1*pi*n-0.5*pi)+2*sin(0.7*pi*n);
(d)
x=3*sin(1.3*pi*n-4*cos(0.3*pi*n+0.45*pi));
(e)
x=5*sin(1.2*pi*n+0.65*pi)+4*sin(0.8*pi*n)-cos(0.8*pi*n);
(f)
x=mod(n,6);
(b)
(c)
(d)
(e)
(f)
M2.6
Writeamatlabprogramtoplotacontinuous-timesinusoidalsignalanditssampledversionandverifyfigure2.19.Youneedtousetheholdfunctiontokeepbothplots.
fo=input('
FrequencyofsinusoidinHz='
SampligfrequencyinHz='
%产生信号
0.001:
1;
g1=cos(2*pi*fo*t);
plot(t,g1,'
-'
)
时间t'
hold
1:
FT;
gs=cos(2*pi*fo*n/FT);
plot(n/FT,gs,'
o'
holdoff
M3.1
Usingprogram3_1determineandplottherealandimaginarypartsandthemagnitudeandphasespectraofthefollowingDTFTforvariousvaluesofrandθ:
0<
r<
1.
%program3_1
%discrete-timefouriertransformcomputatition
%
k=input('
Numberoffrequencypoints='
num=input('
Numeratorcoefficients='
den=input('
Denominatorcoefficients='
%computerthefrequencyresponse
w=0:
pi/k:
pi;
h=freqz(num,den,w);
%plotthefrequencyresponse
subplot(221)
plot(w/pi,real(h));
grid
title('
realpart'
\omega/\pi'
Amplitude'
subplot(222)
plot(w/pi,imag(h));
imaginarypart'
subplot(223)
plot(w/pi,abs(h));
magnitudespectrum'
magnitude'
subplot(224)
plot(w/pi,angle(h));
phasespectrum'
phase,radians'
(a)r=0.8θ=π/6
(b)r=0.6θ=π/3
M3.4
UsingmatlabverifythefollowinggeneralpropertiesoftheDTFTaslistedinTable3.2:
(a)Linearity,(b)time-shifting,(c)frequency-shifting,(d)differentiation-in-frequency,(e)convolution,(f)modulation,and(g)Parseval’srelation.Sincealldatainmatlabhavetobefinite-lengthvectors,thesequencestobeusedtoverifythepropertiesarethusrestrictedtobeoffinitelength.
%先定义两个信号
Thelengthofthesequence='
k=0:
N-1;
%g为正弦信号
g=2*sin(2*pi*k/(N/2));
%h为余弦信号
h=3*cos(2*pi*k/(N/2));
[G,w]=freqz(g,1);
[H,w]=freqz(h,1);
%*************************************************************************%
%线性性质
alpha=0.5;
beta=0.25;
y=alpha*g+beta*h;
[Y,w]=freqz(y,1);
figure
(1);
subplot(211),plot(w/pi,abs(Y));
|Y(e^j^\omega)|'
线性叠加后的频率特性'
grid;
%画出Y的频率特性
subplot(212),plot(w/pi,alpha*abs(G)+beta*abs(H));
\alpha|G(e^j^\omega)|+\beta|H(e^j^\omega)|'
线性叠加前的频率特性'
%画出alpha*G+beta*H的频率特性
%时移性质
n0=10;
%时移10个的单位
y2=[zeros([1,n0])g];
[Y2,w]=freqz(y2,1);
G0=exp(-j*w*n0).*G;
figure
(2);
subplot(211),plot(w/pi,abs(G0));
|G0(e^j^\omega)|'
G0的频率特性'
%画出G0的频率特性
subplot(212),plot(w/pi,abs(Y2));
|Y2(e^j^\omega)|'
Y2的频率特性'
%画出Y2的频率特性
%频移特性
w0=pi/2;
%频移pi/2
r=256;
%thevalueofw0intermsofnumberofsamples
y3=g.*exp(j*w0*k);
[Y3,w]=freqz(y3,1);
%对采样的512个点分别进行减少pi/2,从而生成G(exp(w-w0))
511;
w=-w0+pi*k/512;
G1=freqz(g,1,w);
figure(3);
subplot(211),plot(w/pi,abs(Y3));
|Y3(e^j^\omega)|'
Y3的频率特性'
%画出Y3的频率特性
subplot(212),plot(w/pi,abs(G1));
|G1(e^j^\omega)|'
G1的频率特性'
%画出G1的频率特性
%频域微分
y4=k.*g;
[Y4,w]=freqz(y4,1);
%在频域进行微分
y0=((-1).^k).*g;
G2=[G(2:
512)'
sum(y0)]'
;
delG=(G2-G)*512/pi;
figure(4);
subplot(211),plot(w/pi,abs(Y4));
|Y4(e^j^\omega)|'
Y4的频率特性'
%画出Y4的频率特性
subplot(212),plot(w/pi,abs(delG));
|delG(e^j^\omega)|'
delG的频率特性'
%画出delG的频率特性
%相乘性质
y5=conv(g,h);
%时域卷积
[Y5,w]=freqz(y5,1);
figure(5);
subplot(211),plot(w/pi,abs(Y5));
|Y5(e^j^\omega)|'
Y5的频率特性'
%画出Y5的频率特性
subplot(212),plot(w/pi,abs(G.*H));
%频域乘积
|G.*H(e^j^\omega)|'
G.*H的频率特性'
%画出G.*H的频率特性
%帕斯瓦尔定理
y6=g.*h;
%对于freqz函数,在0到2pi直接取样
[Y6,w]=freqz(y6,1,512,'
whole'
[G0,w]=freqz(g,1,512,'
[H0,w]=freqz(h,1,512,'
%Evaluatethesamplevalueatw=pi/2
%andverifywithY6atpi/2
H1=[fliplr(H0(1:
129)'
)fliplr(H0(130:
)]'
val=1/(512)*sum(G0.*H1);
%ComparevalwithY6(129)i.esampleatpi/2
%Canextendthistootherpointssimilarly
%Parsevalstheorem
val1=sum(g.*conj(h));
val2=sum(G0.*conj(H0))/512;
%Comapreval1withval2
M3.8
UsingmatlabcomputetheN-pointDFTsofthelength-NsequencesofProblem3.12forN=3,5,7,and10.CompareyourresultswiththatobtainedbyevaluatingtheDTFTscomputedinProblem3.12atω=2pik/N,k=0,1,……N-1.
%用户定义N的长度
ThevalueofN='
k=-N:
N;
y1=ones([1,2*N+1]);
w=0:
2*pi/255:
2*pi;
Y1=freqz(y1,1,w);
%对y1做傅里叶变换
Y1dft=fft(y1);
2*N;
plot(w/pi,abs(Y1),k*2/(2*N+1),abs(Y1dft),'
归一化频率'
(a)clf;
Normalizedfrequency'
(b)%用户定义N的长度
y2=y1-abs(k)/N;
Y2=freqz(y2,1,w);
Y2dft=fft(y2);
plot(w/pi,abs(Y2),k*2/(2*N+1),abs(Y2dft),'
(c)%用户定义N的长度
y3=cos(pi*k/(2*N));
Y3=freqz(y3,1,w);
Y3dft=fft(y3);
plot(w/pi,abs(Y3),k*2/(2*N+1),abs(Y3dft),'
(a)N=3
N=5
N=7
N=10
(b)N=3
(c)N=3
M3.19
UsingProgram3_10determinethez-transformasaratiooftwopolynomialsinz-1fromeachofthepartial-fractionexpansionslistedbelow:
%Program3_10
%Partical-FractionExpansiontorationalz-Transform
r=input('
Typeintheresidues='
p=input('
Typeinthepoles='
k=input('
Typeintheconstants='
[num,den]=residuez(r,p,k);
disp('
Numberatorpolynominalcoefficients'
disp(num)
Denominatorpolynomialcoefficients'
disp(den)
M4.6
PlotthemagnitudeandphaseresponsesofthecausalIIRdigitaltransferfunction
Whattypeoffilterdoesthistransferfunctionrepresent?
Determinethedifferenceequationrepresentationoftheabovetransferfunction.
b=[0.0534-0.00088644-0.000886440.0534];
a=[1-2.12911.7833863-0.5434631];
figure
(1)
freqz(b,a);
figure
(2)
[H,w]=freqz(b,a);
plot(w/pi,abs(H)),grid;
NormalizedFrequency(\times\pirad/sample)'
),
Magnitude'
幅度化成真值之后:
4.结果分
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