北京交通大学数字信号处理matlab习题问题详解钱my文档格式.docx
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北京交通大学数字信号处理matlab习题问题详解钱my文档格式.docx
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,t,g2,'
g'
g2(t)'
subplot(4,1,3);
plot(k,h3,'
b.'
t,g3,'
b'
g3(t)'
subplot(4,1,4);
plot(t,g1,'
k,h1,'
k,h2,'
k,h3,'
)
g(t)'
legend('
'
图像:
M1-2
(1)代码:
b=[1];
a=[1-1.8450.850586];
w=linspace(0,2*pi,200);
y=filter(b,a,w);
plot(w,y);
单位脉冲响应'
Normalizedfrequency'
%b=[1];
%a=[1-1.8450.850586];
h=impz(b,a,21);
%figure
(1);
stem(0:
20,h);
(2)代码:
a=[1-1.850.85];
figure
(1);
M1-3
x=firls(511,[00.40.4041],[1100]);
k=linspace(0,1,512);
stem(k,x);
k1=0.4*pi;
y1=x.*cos(k1*k);
A=abs(y1);
plot(A);
k2=0.8*pi;
y2=x.*cos(k2*k);
B=abs(y2);
plot(B);
k3=0.9*pi;
y3=x.*cos(k3*k);
C=abs(y3);
plot(C);
k4=pi;
y4=x.*cos(k4*k);
D=abs(y4);
plot(D);
M1-4
b=[11];
a=2;
w=linspace(0,pi,512);
H1=freqz(b,a,w);
plot(w/pi,unwrap(abs(H1)),'
holdon
b1=[1.8];
a1=[1-0.8];
H2=freqz(b1,a1,w);
plot(w/pi,unwrap(abs(H2)),'
b2=conv(b,b1);
a2=conv(a,a1);
H3=freqz(b2,a2,w);
plot(w/pi,unwrap(abs(H3),'
));
幅度'
M1-5
b1=[0.05340.0534];
b2=[12.03322.0169-1.01661];
a1=[1-0.683];
a2=[1-1.46610.7957];
b=conv(b1,b2);
a=conv(a1,a2);
w=linspace(0,pi,200);
H=freqz(b,a,w);
subplot(2,1,1);
plot(w/pi,abs(H));
subplot(2,1,2);
plot(w,angle(H));
相位'
b1=[1-21];
b2=[1-21];
a1=[1-1.4990.8482];
a2=[1-1.55480.6493];
M1-6
b=[120.99];
a=[11.550.6];
plot(w,unwrap(angle(H)),'
holdon;
b1=[1.11.990.9];
a1=[11.550.6];
Hmin=freqz(b1,a1,w);
plot(w,unwrap(angle(Hmin)),'
b2=[0.91.991.1];
a2=[11.550.6];
Hmax=freqz(b2,a2,w);
plot(w,unwrap(angle(Hmax)),'
m'
omega'
2、第二章
M2-1
g=[1-3420-2];
h=[301-121];
l=length(g);
L=2*l-1;
GE=fft(g,L);
HE=fft(h,L);
y1=ifft(GE.*HE);
forn=1:
l
ifn+l<
=L
y2(n)=y1(n)+y1(n+l);
else
y2(n)=y1(n);
end
y2
l-1,y2)
k'
y(k)'
title('
循环卷积'
)
结果:
y2=
6.0000-3.000017.0000-2.00007.0000-13.0000
k=0:
5;
x=cos(pi.*k./2);
y=3.^k;
l=length(x);
GE=fft(x,L);
HE=fft(y,L);
l
=L
y’(k)'
-71.0000-213.000089.0000267.000073.0000219.0000
M2-2
N=10;
k=-N:
N;
x=cos(k.*pi./(2*N));
W=linspace(-pi,pi,512);
X=zeros(1,length(W));
fork=-N:
N
X1=x(k+N+1).*exp(-j.*W.*k);
X=X+X1;
plot(W,abs(X))
W'
abs(X)'
X_21=fft(x,21);
L=-10:
10;
W=linspace(-pi,pi,1024);
N
plot(W,abs(X));
plot(2*pi*L/21,fftshift(abs(X_21)),'
o'
M2-3
N=64;
L=1024;
f1=100;
f2=120;
fs=800;
A=1;
B1=1;
B2=0.5;
B3=0.25;
B4=0.05;
T=1/fs;
ws=2*pi*fs;
N-1;
x1=A*cos(2*pi*f1*T*k)+B1*cos(2*pi*f2*T*k);
x2=A*cos(2*pi*f1*T*k)+B2*cos(2*pi*f2*T*k);
x3=A*cos(2*pi*f1*T*k)+B3*cos(2*pi*f2*T*k);
x4=A*cos(2*pi*f1*T*k)+B4*cos(2*pi*f2*T*k);
hf=(hamming(N))'
;
x1=x1.*hf;
x2=x2.*hf;
x3=x3.*hf;
x4=x4.*hf;
X1=fftshift(fft(x1,L));
X2=fftshift(fft(x2,L));
X3=fftshift(fft(x3,L));
X4=fftshift(fft(x4,L));
W=T*(-ws/2+(0:
L-1)*ws/L)/(2*pi);
subplot(2,2,1);
plot(W,abs(X1));
A=1,B=1'
X1'
subplot(2,2,2);
F2=120HZ时:
F2=140HZ时:
F2=160HZ时:
M2-4
W0=2*pi/15;
W1=2.3*pi/15;
x=cos(W0*k)+0.75*cos(W1*k);
X=fft(x);
plot(k/N,abs(X));
gridon;
64点FFT'
X=fft(x,L);
plot((0:
L-1)/N,abs(X));
1024点FFT'
M2-5:
fs=100;
Ts=1/fs;
N=fs;
x=exp(-3*Ts*(0:
N-1));
y=fft(x,N);
l=length(y);
k=linspace(-ws/2,ws/2,l);
plot(k,Ts*fftshift(abs(y)),'
b:
'
w=linspace(-ws/2,ws/2,1024);
y1=sqrt(1./(9+w.^2));
plot(w,y1,'
fs=100Hz时的频谱'
近似值'
实际值'
fs=10HZ时:
fs=50Hz时:
fs=100HZ时:
M2-6
Ts=0.5;
N=4;
N0=64;
k=(-N/2:
(N/2))*Ts;
x=exp(-pi*(k).^2);
X=Ts*fftshift(fft(x,N0));
w=-pi/Ts:
2*pi/N0/Ts:
(pi-2*pi/N0)/Ts;
XT=(pi/pi)^0.5*exp(-w.^2/4/pi);
subplot(2,1,1)
plot(w/pi,abs(X),'
-o'
w/pi,XT);
\omega/\pi'
X(j\omega)'
试验值'
理论值'
title(['
Ts='
num2str(Ts)'
'
N='
num2str(N)]);
subplot(2,1,2)
plot(w/pi,abs(X)-XT)
实验误差'
Ts=1,N=2:
Ts=0.5,N=2:
Ts=0.5,N=4:
3、第四章
M4-1
WP=10;
WS=2;
Ap=1;
As=40;
wp=1/WP;
ws=1/WS;
w0=1;
B=2;
[N,Wc]=cheb1ord(wp,ws,Ap,As,'
s'
[num,den]=cheby1(N,Ap,Wc,'
[numt,dent]=lp2hp(num,den,1);
w=linspace(1,12,1000);
h=freqs(numt,dent,w);
plot(w,20*log10(abs(h)));
grid;
Frequencyinrad/s'
GainindB'
M4-2
wp=1;
ws=3.3182;
As=32;
w0=sqrt(48);
[N,Wc]=buttord(wp,ws,Ap,As,'
[num,den]=butter(N,Wc,'
[numt,dent]=lp2bp(num,den,w0,B);
w=linspace(2,12,1000);
M4-3
(2)代码:
[N,Wc]=cheb2ord(wp,ws,Ap,As,'
[num,den]=cheby2(N,Ap,Wc,'
(3)代码:
w0=sqrt(48)
[N,Wc]=ellipord(wp,ws,Ap,As,'
[num,den]=ellip(N,Ap,As,Wc,'
M4-4
As=10;
wp1=6;
wp2=13;
ws1=9;
ws2=11;
B=ws2-ws1;
w0=sqrt(ws1*ws2);
wLp1=B*wp1/(w0*w0-wp1*wp1);
wLp2=B*wp2/(w0*w0-wp2*wp2);
wLp=max(abs(wLp1),abs(wLp2));
[N,Wc]=buttord(wLp,1,Ap,As,'
);
[numt,dent]=lp2bs(num,den,w0,B);
w=linspace(5,14,1000);
plot(w,20*log10(abs(h)));
w=[wp1ws1ws2wp2];
set(gca,'
xtick'
w);
grid;
A=-20*log10(abs(h));
M4-5
[N,Wc]=ellipord(wLp,1,Ap,As,'
M4-6
Wp=0.1*pi;
Ws=0.4*pi;
As=25;
Fs=1
wp=Wp*Fs;
ws=Ws*Fs;
N=buttord(wp,ws,Ap,As,'
wc=wp/(10^(0.1*Ap)-1)^(1/2/N);
[numa,dena]=butter(N,wc,'
[numd,dend]=impinvar(numa,dena,Fs);
h=freqz(numd,dend,w);
norm=max(abs(h));
numd=numd/norm;
plot(w/pi,20*log10(abs(h)/norm));
w=[WpWs];
fprintf('
Ap=%.4f\n'
-20*log10(abs(h
(1))));
As=%.4f\n'
-20*log10(abs(h
(2))));
WP=0.1*pi;
WS=0.4*pi;
Fs=1;
wp=WP*Fs;
ws=WS*Fs;
N=cheb2ord(wp,ws,Ap,As,'
[numa,dena]=cheby2(N,As,wc,'
plot(w/pi,20*log10(abs(h)/norm))
w=[wpws];
M4-7
代码:
Wp=0.2*pi;
As=15;
[N,wc]=buttord(wp,ws,Ap,As,'
[num,dend]=impinvar(numa,dena,Fs);
w=linspace(0,pi,1024);
h=freqz(num,dend,w);
plot(w/pi
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