Jacqueline asked . 2021-03-10

Why do I receive two different responses when I try to discretize the same analog filter using the ELLIP

Fs = 2e9; 

FN = Fs/2;

fp = 0.4*FN; 

fs = 0.42*FN;

wp = fp*2*pi; 

ws = fs*2*pi;

Ap = 1.2; 

As = 100;

% Calculate filter coefficients and frequency responses

[N, wc] = ellipord(wp, ws, Ap, As, 's'); 

[B, A] = ellip(N, Ap, As, wc, 's');

[bBZT, aBZT] = bilinear(B, A, Fs); 

[Ha, wa] = freqs(B, A);

figure;

plot(wa/(2*pi), 20*log10(abs(Ha)))  

[HB, fB]=freqz(bBZT, aBZT, 512, Fs);

hold on

plot(fB, 20*log10(abs(HB)), 'r'); 

legend('Analog Response', 'Digital reponse');

Fs = 2e9; 

FN = Fs/2;

fp = 0.4*FN; 

fs = 0.42*FN;

wp = fp*2*pi;

ws = fs*2*pi;

Ap = 1.2; 

As = 100;

% Calculate filter coefficients and frequency responses

[N, wc] = ellipord(wp, ws, Ap, As,'s'); 

[z, p, k] = ellipap(N, Ap, As); 

[A, B, C, D] = zp2ss(z, p, k); 

[At, Bt, Ct, Dt] = lp2lp(A, B, C, D, wc); 

[Bs, As] = ss2tf(At, Bt, Ct, Dt);

[Ad, Bd, Cd, Dd] = bilinear(At, Bt, Ct, Dt, Fs);

[bd, ad] = ss2tf(Ad, Bd, Cd, Dd);

[Ha, wa]=freqs(Bs, As);

figure; 

plot(wa/(2*pi), 20*log10(abs(Ha))) 

hold on

[HB, fB]=freqz(bd, ad, 512, Fs);

plot(fB, 20*log10(abs(HB)), 'r'); 

legend('Analog Response(using Analog prototype)', 'Digital response (using Analog prototype)');

matlab , signal , signal processing , filter design