freqpoles.py

# FREQPOLES - Pole set generation for the PARFILTDES function.
#   [P]=freqpoles(FR,Fs) creates poles from the given frequency vector
#   FR with sampling frequency Fs such that the frequency responses
#   of the second-order basis functions cross approximatelly at their
#   -3 dB point.
#   (See the equations in my 128th AES Convention paper.)
#
#   [P]=freqpoles(FR,Fs,Q) creates poles from the given frequency vector
#   FR with sampling frequency Fs but it uses the quality factors 
#   given in Q vector to set the radius of the poles. (-3dB bandwidth
#   is DeltaF=FR/Q.)
#
#   C. Balazs Bank, 2010.

import numpy as np

def freqpoles(fr, Fs = 44100, Q = None):

	# discrete pole frequencies
	wp = 2 * np.pi * fr / Fs 

	dwp = []
	if Q is None:
		pnum = wp.size
		dwp = np.zeros(pnum)
		for k in range(1, pnum-1):
			dwp[k] = (wp[k+1] - wp[k-1])/2
		dwp[0] = wp[1] - wp[0]
		dwp[pnum-1] = wp[pnum-1] - wp[pnum-2]
	else:
		dwp = wp / Q
		
	p = np.exp(-dwp/2) * np.exp(1j * wp)
	
	return np.hstack([p, p.conj()])