How to calculate prewardped frequency in analog domain

How to approach the problem of calculating prewarped frequency in analog domain if I have to use bilinear z-transform? Sampling frequency of 20kHz and band edges of IIR BPF digital filter as 4 and 7khz.

How to do this in matlab?

Answer 1

[Star Strider]

The prewarping frequency in the analog domain is whatever you want it to be. I usually choose the corner frequency of a highpass or lowpass filter, or the centre frequency of the bandpass or stopband in those filters. For a filter with multiple passbands and stopbands (rare), I choose the frequency that is half the Nyquist frequency. That also works if you simply can’t decide.

Essentially, it needs to be whatever will produce the best filter in the discrete domain after the transformation. As with everything else in signal processing, this usually requires some experimentation to get the result you want. Always use the freqz function to see what your filter is doing before you actually filter with it. And always use the filtfilt function to do the actual filtering.

[variksla peoli]

Would you be so kind to add some matlab code that is using bilinear z-transform to calculate prewarped frequency in analog domain?

[Star Strider]

This works (adapted from the example in the documentation for bilinear):

Fs = 0.5;                               % Sampling frequency
Fp = 6;                                 % Prewarping Frequency
[z,p,k] = ellipap(22,21,90);            % Lowpass filter prototype
[num,den] = zp2tf(z,p,k);               % Convert to transfer function form
[numd,dend] = bilinear(num,den,Fs,Fp);  % Analog To Digital Conversion With Prewarping
[sos,g] = tf2sos(numd,dend);

freqz(sos, 2^16, Fs)                    % Visualize the filter
set(subplot(2,1,1), 'XLim',[0 0.1])     % ‘Zoom’ X-Axis
set(subplot(2,1,2), 'XLim',[0 0.1])     % ‘Zoom’ X-Axis

[variksla peoli]

You didn't consider band edges of 4 and 7Khz.

[Star Strider]

You can only prewarp at one frequency.

Choose the one you want. I chose this one arbitrarily for demonstration purposes.