[python] How to implement band-pass Butterworth filter with Scipy.signal.butter

For a bandpass filter, ws is a tuple containing the lower and upper corner frequencies. These represent the digital frequency where the filter response is 3 dB less than the passband.

wp is a tuple containing the stop band digital frequencies. They represent the location where the maximum attenuation begins.

gpass is the maximum attenutation in the passband in dB while gstop is the attentuation in the stopbands.

Say, for example, you wanted to design a filter for a sampling rate of 8000 samples/sec having corner frequencies of 300 and 3100 Hz. The Nyquist frequency is the sample rate divided by two, or in this example, 4000 Hz. The equivalent digital frequency is 1.0. The two corner frequencies are then 300/4000 and 3100/4000.

Now lets say you wanted the stopbands to be down 30 dB +/- 100 Hz from the corner frequencies. Thus, your stopbands would start at 200 and 3200 Hz resulting in the digital frequencies of 200/4000 and 3200/4000.

To create your filter, you'd call buttord as

fs = 8000.0
fso2 = fs/2
N,wn = scipy.signal.buttord(ws=[300/fso2,3100/fso2], wp=[200/fs02,3200/fs02],
   gpass=0.0, gstop=30.0)

The length of the resulting filter will be dependent upon the depth of the stop bands and the steepness of the response curve which is determined by the difference between the corner frequency and stopband frequency.

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