## Digital Filter from coefficients

### gbernardi (view profile)

on 13 May 2011
Hello everybody. I am trying to do some review exercises about filters. In particular, I'm trying to convert a filter from analog to digital. I'm working with an analog filter (a simple bandpass filter) whose transfer function can be described by:
TF = 1./(1+ (1j*Q*(f./fc - fc./f)));
where f is the frequency vector, fc is the center frequency of the filter and Q is the Q-factor.
I just wanted to have the same filter in a digital domain form (I know that I could also use invfreqz using TF as a parameter but I don't want to do it that way), so I thought I could just extract the coefficients from the TF in the continuous domain, which are:
a1 = [Q*1i fcs(k) -Q*1i*fcs(k)^2];
b1 = [fcs(k) 0];
use the bilinear transformation
[numd,dend] = bilinear(b1,a1,8e3);
and finally get the frequency response of it by
h1 = freqz(numd, dend, f,8e3);
but the frequency response I obtain here is different from the previous one as it appears to be shifted in frequency when I plot them:
plot(f,20*log10(abs(TF)))
hold on;
plot(f,20*log10(abs(h1)),'m')
I'm sure I'm doing some silly mistakes, but I'd like to have some hints ;)