butter() not normalized

Hallo,

ist es möglich die Übertragungsfunktion, die aus den berechneten Koeffizienten der butter() Funktion entsteht NICHT normiert darzustellen, sondern in Hz oder kHz?

Liebe Grüße und vielen Dank!

[Jan]

The filter parameters itself do not have the frequency Hz or kHz. You can filter meters and gallons, Canadian Dollar and colors also. Therefore it is not clear to me yet, what you are exactly asking for.

Answer 1

[Star Strider]

In the buttord, butter (and similar functions for other filter designs), the frequencies you pass to the functions are normalised to (0,pi) radians, corresponding to (0,Fn), where ‘Fn’ is the Nyquist frequency, which is half your sampling frequency ‘Fs’.

So the frequencies you pass to the filter functions are actually dimensionless, in that they are calculated by dividing your desired frequency by your Nyquist frequency.

For example, if you have a sampling frequency of 5000 Hz and you want to design a lowpass filter with a cutoff frequency of 750 Hz, the frequency calculations would be:

Fs = 5000;
Fn = Fs/2;
Fp =  750;
Wp = Fp/Fn;

where ‘Fp’ and ‘Wp’ are the original and normalised passband frequencies, respectively. The same calculations apply to defining the stopband ‘Ws’ frequencies. You use ‘Wp’ and ‘Ws’ as arguments to the filter design functions.