Converting from samplerate/cutoff frequency to pi-radians/sample in a discrete time sampled IIR filter system

Question

I am working on doing some digital filter work using Python and Numpy/Scipy.

I'm using scipy.signal.iirdesign to generate my filter coefficents, but it requires the filter passband coefficents in a format I am not familiar with

wp, ws : float

  Passband and stopband edge frequencies, normalized from 0 to 1 (1 corresponds 
      to pi radians / sample). 
  For example:
  Lowpass: wp = 0.2, ws = 0.3
  Highpass: wp = 0.3, ws = 0.2

(from here)

I'm not familiar with digital filters (I'm coming from a hardware design background). In an analog context, I would determine the desired slope and the 3db down point, and calculate component values from that.

In this context, how do I take a known sample rate, a desired corner frequency, and a desired rolloff, and calculate the wp, ws values from that?

(This might be more appropriate for math.stackexchange. I'm not sure)

Answer 1

If your sampling rate is fs, the Nyquist rate is fs/2. This represents the highest representable frequency you can have without aliasing. It is also equivalent to the normalized value of 1 referred to by the documentation. Therefore, if you are designing a low pass filter with a corner frequency of fc, you'd enter it as fc / (fs/2).

For example, you have fs=8000 so fs/2=4000. You want a low pass filter with a corner frequency of 3100 and a stop band frequency of 3300. The resulting values would be wp=fc/(fs/2)=3100/4000. The stopband frequency would be 3300/4000.

Make sense?