%用低通濾波器濾去高頻信號
n=0:0.0001:1;
fs=10e3;
xl=sin(2*pi*20*n);
xm=sin(2*pi*2e3*n);
xh=sin(2*pi*4.5e3*n);
x=xl+xm+xh;
figure(1)
subplot(2,2,1),plot(n,xl),xlabel('n'),ylabel('xl'),title('低頻信號');
subplot(2,2,2),plot(n,xm),xlabel('n'),ylabel('xm'),title('中頻信號');
subplot(2,2,3),plot(n,xh),xlabel('n'),ylabel('xh'),title('高頻信號');
subplot(2,2,4),plot(n,x),xlabel('n'),ylabel('x'),title('疊加信號');
M=8192;
y=fft(x,8192);
Ay=abs(y(1:M/2));
k=(0:M/2-1)*fs/M;
figure(2)
subplot(1,1,1),plot(k,Ay),xlabel('頻率(Hz)'),ylabel('Ay');
title('濾波前頻譜'),axis([-100,5000,0,3500]);
fl=3000;df=500;rp=1;rs=60;fs=10e3;fn=fs/2;
[nb,wn]=buttord(fl/fn,[fl+df]/fn,rp,rs);
[b,a]=butter(nb,wn);
[h1,f1]=freqz(b,a,100,fs);
figure(3)
plot(f1,20*log10(abs(h1))),axis([0,5000,-300,100]);
xlabel('頻率(Hz)'),ylabel('幅度(dB)'),title('低通濾波器波形');
X1=filter(b,a,x);
z=fft(X1,8192);
Az=abs(z(1:M/2));
figure(4)
subplot(2,1,1),plot(X1(1:M/2+1)),xlabel('n'),ylabel('X'),title('濾波后波形');
subplot(2,1,2),plot(k,Az),xlabel('頻率(Hz)'),ylabel('Az');
title('濾波后頻譜'),axis([-100,5000,0,3500]);