数字信号.docx
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数字信号.docx
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数字信号
第三次试验
1代码clear
N=12;
fork=0:
N-1
f(k+1)=0;
form=0:
N-1
f(k+1)=sin(m*pi/5).*exp(-i*2*pi*k*m/N)+f(k+1);
end
end
k=0:
N-1;
figure
subplot(2,1,1)
stem(k,sin(k*pi/5))
gridon
title('ÔÐźÅ')
subplot(2,1,2)
stem(k,f)
gridon
title('ÔÐźŵÄDFT')
2代码
clear
x=[1,2,3,4,5];
h=[2,3,4,6];
n=length(x)+length(h)-1;
x1=[xzeros(1,length(h)-1)];
h1=[hzeros(1,length(x)-1)];
fork=0:
n-1
x2(k+1)=0;
forj=0:
n-1
x2(k+1)=x1(j+1).*exp((-i)*2*pi*k*j/n)+x2(k+1);
end
end
fork=0:
n-1
h2(k+1)=0;
forj=0:
n-1
h2(k+1)=h1(j+1).*exp(-i*2*pi*k*j/n)+h2(k+1);
end
end
fork=0:
n-1
y(k+1)=x2(k+1).*h2(k+1);
end
fork=0:
n-1
y1(k+1)=0;
forj=0:
n-1
y1(k+1)=y(j+1).*exp(i*2*pi*k*j/n)/n+y1(k+1);
end
end
k=0:
n-1;
stem(k,y1(k+1))
title('ÀûÓÃDFTµÃµ½µÄÏßÐÔ¾í»ý')
figure
g=conv(x,h);
k=0:
n-1;
stem(k,g)
title('µ÷Óú¯ÊýµÃµ½¾í»ý')
3代码
figure
ts=1;
t=0:
ts:
99;
x=3*sin(t*pi/6)+5*cos(t*pi/5);
subplot(2,1,1)
stem(t,x)
title('Ts=1')
N=100;
fork=0:
N-1
f(k+1)=0;
form=0:
N-1
f(k+1)=x(m+1).*exp(-i*2*pi*k*m/N)+f(k+1);
end
end
subplot(2,1,2)
k=0:
N-1;
stem(k,f)
figure
t=0:
2*ts:
199;
x=3*sin(t*pi/6)+5*cos(t*pi/5);
subplot(2,1,1)
stem(t,x)
title('Ts=2')
N=100;
fork=0:
N-1
f(k+1)=0;
form=0:
N-1
f(k+1)=x(m+1).*exp(-i*2*pi*k*m/N)+f(k+1);
end
end
subplot(2,1,2)
k=0:
N-1;
stem(k,f)
figure
ts=0.5;
t=0:
ts:
99*ts;
x=3*sin(t*pi/6)+5*cos(t*pi/5);
subplot(2,1,1)
stem(t,x)
title('Ts=0.5')
N=100;
fork=0:
N-1
f(k+1)=0;
form=0:
N-1
f(k+1)=x(m+1).*exp(-i*2*pi*k*m/N)+f(k+1);
end
end
subplot(2,1,2)
k=0:
N-1;
stem(k,f)
N=100;
t=0:
N-1;
x=3*sin(t*pi/6)+5*cos(t*pi/5);
fork=0:
N-1
f(k+1)=0;
form=0:
N-1
f(k+1)=x(m+1).*exp(-i*2*pi*k*m/N)+f(k+1);
end
end
subplot(3,1,1)
k=0:
N-1;
stem(k,f(k+1))
title('N=100')
N=200;
t=0:
N-1;
x=3*sin(t*pi/6)+5*cos(t*pi/5);
fork=0:
N-1
f(k+1)=0;
form=0:
N-1
f(k+1)=x(m+1).*exp(-i*2*pi*k*m/N)+f(k+1);
end
end
subplot(3,1,2)
k=0:
N-1;
stem(k,f(k+1))
title('N=200')
N=500;
t=0:
N-1;
x=3*sin(t*pi/6)+5*cos(t*pi/5);
fork=0:
N-1
f(k+1)=0;
form=0:
N-1
f(k+1)=x(m+1).*exp(-i*2*pi*k*m/N)+f(k+1);
end
end
subplot(3,1,3)
k=0:
N-1;
stem(k,f(k+1))
title('N=500')
clear
N=100;
t=0:
N-1;
x=3*sin(t*pi/6)+5*cos(t*pi/5);
fork=0:
N-1
f(k+1)=0;
form=0:
N-1
f(k+1)=x(m+1).*exp(-i*2*pi*k*m/N)+f(k+1);
end
end
subplot(3,1,1)
k=0:
N-1;
stem(k,f(k+1))
title('ÔÐźŹ²100¸öµã')
N=200;
x=[xzeros(1,100)];
fork=0:
N-1
f(k+1)=0;
form=0:
N-1
f(k+1)=x(m+1).*exp(-i*2*pi*k*m/N)+f(k+1);
end
end
subplot(3,1,2)
k=0:
N-1;
stem(k,f(k+1))
title('ÔÐźŲ¹ÁË100¸öÁã')
N=400;
x=[xzeros(1,400)];
fork=0:
N-1
f(k+1)=0;
form=0:
N-1
f(k+1)=x(m+1).*exp(-i*2*pi*k*m/N)+f(k+1);
end
end
subplot(3,1,3)
k=0:
N-1;
stem(k,f(k+1))
title('ÔÐźŲ¹ÁË400¸öÁã')
第四次试验
1,图形缩小
clear
[x,cmap]=imread('F:
\14.jpg');
y=rgb2gray(x);
imshow(y);
figure
w=fft2(y);
W=[w(1:
128,1:
128)w(1:
128,384:
512);
w(384:
512,1:
128)w(384:
512,384:
512)];
d=ifft2(W);
imshow(uint8(d/4))
原图形
缩小后的图形
图形放大
clear
[x,cmap]=imread('F:
\13.jpg');
y=rgb2gray(x);
imshow(y);
figure
w=fft2(y);
W=[w(1:
128,1:
128)zeros(256/2,512/2)w(1:
128,129:
256);
zeros(512/2,256/2)zeros(512/2,512/2)zeros(512/2,256/2);
w(129:
256,1:
128)zeros(256/2,512/2)w(129:
256,129:
256)];
d=ifft2(W);
imshow(uint8(d*4))
原图形
放大后的
2分块转化
clear
[x,cmap]=imread('F:
\14.jpg');
y=rgb2gray(x);
imshow(y);
w=fft2(y);
W1=[w(1:
128,129+257:
512)w(1:
128,1:
128)
w(129+257:
512,129+257:
512)w(129+257:
512,1:
128)];
W2=[w(1:
128,129:
129+256);w(129+257:
512,129:
129+256)];
W3=[w(129:
129+257,1:
128)w(129:
129+257,129+257:
512)];
W4=w(129:
129+256,129:
129+256);
d1=ifft2(W1);
d2=ifft2(W2);
d3=ifft2(W3);
d4=ifft2(W4);
figure
%subplot(2,2,1)
imshow(uint8(d1/4))
figure
imshow(uint8(d2))
figure
imshow(uint8(d3))
figure
imshow(uint8(d4))
L_L
L_H
H_L
H_H
第五次试验
1,加窗函数
代码clear
n=1;
fork=-20:
20
h(n)=0;
form=-pi:
0.01:
pi
h(n)=h(n)+((-1-2*m/pi)*(u(m+1.001*pi)-u(m+pi/2))+(1+2*m/pi)*(u(m+pi/2)-u(m))+(1-2*m/pi)*(u(m)-u(m-pi/2))+(-1+2*m/pi)*(u(m-pi/2)-u(m-1.001*pi)))*exp(i*m*k)/(2*pi)/100;
end
n=n+1;
end
k=-20:
20;
stem(k,abs(h))
figure
k=-16:
16;
y=hanning(33);
stem(k,y)
n=5:
37;
y1(n)=abs(h(n));
forn=5:
37
s(n-4)=abs(h(n))*y(n-4);
end
figure
n=5:
37;
stem(n-4,s(n-4))
figure
n=1;
fork=0:
0.01:
2*pi
x(n)=0;
fora=1:
33
x(n)=x(n)+s(a)*exp(-i*(a-1)*k);
end
n=n+1;
end
k=0:
0.01:
2*pi;
plot(k,abs(x))
设计的滤波器
2频率抽样法
clear
N=33;
fork=1:
33
M=(N-1)*k*pi/N;
m=2*pi*k/N;
H(k)=((-1-2*(m-2*pi)/pi)*(u(m-pi)-u(m-1.5*pi))+(1+2*(m-2*pi)/pi)*(u(m-1.5*pi)-u(m-2*pi))+(1-2*m/pi)*(u(m)-u(m-pi/2))+(-1+2*m/pi)*(u(m-pi/2)-u(m-pi)))*exp(-i*M);
end
forn=1:
33
h(n)=0;
fork=1:
33
h(n)=h(n)+H(k)*exp(i*2*pi*k*n/N)/N;
end
end
n=1:
33;
stem(n,h(n))
title('ËùÇóµÄh£¨n£©')
clear
N=33;
fork=1:
33
M=(N-1)*(k-1)*pi/N;
m=2*pi*(k-1)/N;
H(k)=((-1-2*(m-2*pi)/pi)*(u(m-pi)-u(m-1.5*pi))+(1+2*(m-2*pi)/pi)*(u(m-1.5*pi)-u(m-2.01*pi))+(1-2*m/pi)*(u(m+0.00000000000001)-u(m-pi/2))+(-1+2*m/pi)*(u(m-pi/2)-u(m-1.001*pi)))*exp(-i*M);
end
figure
n=1;
forb=0:
0.01:
2*pi
h1(n)=0;
fora=1:
33
h1(n)=h1(n)+H(a)*(1-exp(-i*b*N))/(1-exp(i*2*pi*(a-1)/N)*exp(-i*b))/N;
end
n=n+1;
end
b=0:
0.01:
2*pi;
plot(b,abs(h1))
title('ËùÉè¼ÆµÄÂ˲¨Æ÷')
设计的滤波器
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