Why do I receive different results when comparing a digital filter designed

Prashant Kumar answered . 2024-12-21 00:29:04

Wc = tan(pi/2*Fc/(Fs/2)); % Analog prewarped freq. rad/second

Note that this frequency is already in rad/second so the analog design is:

[Bs,As] = butter(4,Wc,'s');

 s=(1-z^(-1))/(1+z^(-1)).

In the BILINEAR function documentation, the following transformation is used:

 s = 2*Fs*(z-1)/(z+1)

which is equivalent to

 s = 2*Fs*(1-z^(-1))/(1+z^(-1)).

[Bz,Az] = bilinear(Bs,As,.5);

using FVTOOL as follows will show two identical filters:

fvtool(B,A,Bz,Az);

Note that if you are uncomfortable with using a different "Fs" for the bilinear transformation, you could use the same "Fs" throughout if you take that into account when prewarping as follows:

Wc = 2*Fs*tan(pi/2*Fc/(Fs/2));
[Bs,As] = butter(4,Wc,'s');
[Bz,Az] = bilinear(Bs,As,Fs);
[B ,A] = butter(4,Fc/(Fs/2));
fvtool(B,A,Bz,Az);

A similar discussion can be found in the documentation by typing the following command in MATLAB 7.0.4 (R14SP2):

web([docroot,'/toolbox/signal/filter15.html'])

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