MATLAB: Designing IIR Filters using Bilinear Transform

cut-offfilterfrequencyiir filters

I have written the following code to design an IIR filter with a cut-off frequency of 800 Hz. However, I'm not getting the desired cut-off in the plot. Can someone tell me where I went wrong ?
clc;
clear all;
close all;
N = 2;
Wc = 800;
FS = 8000;
wc = 2*pi*Wc/FS;
T = 1;
[a, b] = butter(N, wc, 's');
[ad, bd] = bilinear(a, b, T);
freqz(ad,bd,512,8000); 
axis([0 4000 -40 1]);
title('Frequency Response of the Filter')

Best Answer

so final and last version of the answer : 
N = 2;
fc = [500 1000];
FS = 8000;
fcn = 2*fc/FS;
T = 1/FS;
freq = logspace(2,log10(FS/2.56));
% [ad, bd] = butter(N, fcn); % digital version
[a, b] = butter(N, 2*pi*fc, 's'); % analog version
figure(1); % allows log x 


[g,p]  = bode(a,b,2*pi*freq);grid
subplot(2,1,1),semilogx(freq,20*log10(g));
title('Frequency Response of the Filter')
subplot(2,1,2),semilogx(freq,p);grid
[ad, bd] = bilinear(a, b, FS);
figure(2); freqz(ad,bd,freq,FS);  % allows only lin x 
title('Frequency Response of the Filter')
figure(3); % allows log x 
[g,p]  = dbode(ad,bd,1/FS,2*pi*freq);
subplot(2,1,1),semilogx(freq,20*log10(g));grid
title('Frequency Response of the Filter')
subplot(2,1,2),semilogx(freq,p);grid
% axis([0 4000 -40 1]);
[ad, bd] = butter(N, fcn); % digital version
figure(4); % allows log x 
[g,p]  = dbode(ad,bd,1/FS,2*pi*freq);
subplot(2,1,1),semilogx(freq,20*log10(g));grid
title('Frequency Response of the Filter')
subplot(2,1,2),semilogx(freq,p);grid
Related Question