重庆大学通信学院数字信号处理实验第三次打印

1.1

b=[1 6 4];

a=[1 7 10];

w=0:0.1:2*pi*3;

h=freqz(b,a,w);

n=abs(h);

k=angle(h);

subplot(2,1,1);

plot(n);

title('magnitude')

subplot(2,1,2);

plot(k);

title('angle')

1．2

b=ones(1,64);

a=[1];

w=0:0.01:pi;

freqz(b,a,w)

1．3

b=[zeros(1,12) ones(1,64)];

a=[1];

w=0:0.01:pi;

freqz(b,a,w)

2.1

clf;

X=[0 1 2 3 4 5 6 7 8];

N=length(X);

n=0:N-1;

Y=yzyw(X,5);

Xk=fft(X);

Yk=fft(Y);

subplot(2,2,1);

stem(n,abs(Xk));

grid

title('原序列DFT的幅度')

subplot(2,2,2);

stem(n,abs(Yk));

grid

title('圆周移位后序列DFT的幅度');

subplot(2,2,3);

stem(n,angle(Xk));

grid

title('原序列DFT的相位')

subplot(2,2,4);

stem(n,angle(Yk));

grid

title('圆周移位后序列DFT的相位');

2.2

function[xec,xoc]=gedc(x);

N=length(x);

n=0:N-1;

xec=(x+x(mod(-n,N)+1))/2;

xoc=(x-x(mod(-n,N)+1))/2;

N=16;

n=0:15;

x1=cos(pi/4*n);

x2=sin(pi/8*n);

x3=x1+j*x2;

x1k=fft(x1);

x2k=fft(j*x2);

x3k=fft(x3);

[y3kep,y3keo]=gedc(x3k);

subplot(3,2,1)

stem(n,x1k);grid

title('x1的DFT序列');

subplot(3,2,2)

stem(n,x2k);grid

title('x2的DFT序列');

subplot(3,2,3)

stem(n,y3kep);grid

title('x3的DFT圆周共轭对称分量');

subplot(3,2,4)

stem(n,y3keo);grid

title('x3的DFT圆周反共轭对称分量');

subplot(3,2,5)

stem(n,x1k-y3kep);grid

title('x1k-y3kep');

subplot(3,2,6)

stem(n,x2k-y3keo);

title('x2k-y3keo');

2.3

N=16;

n=0:15;

x1=cos(pi/4*n);

x2=sin(pi/8*n);

x3=x1+x2;

x1k=fft(x1);

x2k=fft(-j*x2);

x3k=fft(x3);

subplot(3,2,1)

stem(n,x1k);grid

title('x1的DFT序列');

subplot(3,2,2)

stem(n,x2k);grid

title('x2的DFT序列');

subplot(3,2,3)

stem(n,real(x3k));grid

title('x3的DFT实部');

subplot(3,2,4)

stem(n,imag(x3k));grid

title('x3的DFT虚部');

subplot(3,2,5)

stem(n,x1k-real(x3k));grid

title('x1k-real(x3k)');

subplot(3,2,6)

stem(n,x2k-imag(x3k));

title('x2k-imag(x3k)');

3.1

b=[1 -0.25];

a=[1 -1.86 0.8643 1.5];

[r,p,h]=residuez(b,a);

r =

0.4375 - 0.3228i

0.4375 + 0.3228i

0.1251

>> p

p =

1.2412 + 0.9322i

1.2412 - 0.9322i

-0.6225

>> h

h =

[]

3.2

b=[1 -0.25];

a=[1 -1.86 0.8643 1.5];

[g,t]=impz(b,a);

stem(t,g);

4.1

L=31

n=0:14;

x=0.5.^n;

h=ones(1,15);

x1=[x,zeros(1,L-length(x))];

h1=[h,zeros(1,L-length(h))];

%fft

tic

x1k=fft(x1);

h1k=fft(h1);

y1k=x1k.*h1k;

y=ifft(y1k);

subplot(3,1,1);

stem(y);

axis([0 30 0 2]);

toc

%conv

tic

z=conv(x,h);

subplot(3,1,2);

stem(z);

toc

subplot(3,1,3);

z=[z 0 0]

stem(y-z);

TIME:

L =

31

Elapsed time is 0.008692 seconds.

Elapsed time is 0.007559 seconds.

>>

4.2

L=128

L =

128

Elapsed time is 0.024602 seconds.

Elapsed time is 0.007636 seconds.

clc;

clear;

L=128

n=0:14;

x=0.5.^n;

h=ones(1,15);

x1=[x,zeros(1,L-length(x))];

h1=[h,zeros(1,L-length(h))];

%fft

tic

x1k=fft(x1);

h1k=fft(h1);

y1k=x1k.*h1k;

y=ifft(y1k);

subplot(3,1,1);

stem(y);

axis([0 30 0 2]);

toc

%conv

tic

z=conv(x,h);

subplot(3,1,2);

stem(z);

toc

subplot(3,1,3);

z=[z zeros(1,99)]

stem(y-z);

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