# network synthesis filters import numpy as np def LPB(n): # via: # https://github.com/vinniefalco/DSPFilters/blob/master/shared/DSPFilters/source """n-th order butterworth low-pass filter cascade -3 dB at center frequency.""" series = [] pi2 = np.pi/2 pairs = int(n/2) for i in range(pairs): # magnitude = 1 theta = pi2*(1 + (2*i + 1)/n) real = np.cos(theta) imag = np.sin(theta) num = (0, 0, 1) den = (1, -2*real, real*real + imag*imag) series += [(num, den)] if n % 2: num = (0, 1) den = (1, 1) series += [(num, den)] return series def LPC(n, ripple, type=1): # via: # https://github.com/vinniefalco/DSPFilters/blob/master/shared/DSPFilters/source # FIXME: type 2 has wrong center frequency? """n-th order chebyshev low-pass filter cascade 0 dB at center frequency for type 1. -ripple dB at center frequency for type 2. when ripple=0 and type=1, acts as butterworth.""" series = [] ripple = np.abs(ripple) lin = np.exp(ripple*0.1*np.log(10)) if ripple != 0: if type == 2: eps = np.sqrt(1/(lin - 1)) else: eps = np.sqrt(lin - 1) v0 = np.arcsinh(1/eps)/n else: if type == 2: v0 = 0 # allpass? else: v0 = 1 # butterworth sinh_v0 = -np.sinh(v0) cosh_v0 = np.cosh(v0) fn = np.pi/(2*n) pairs = int(n/2) for i in range(pairs): k = 2*i + 1 theta = (k - n)*fn real = sinh_v0*np.cos(theta) imag = cosh_v0*np.sin(theta) if type == 2: d2 = real*real + imag*imag im = 1/np.cos(k*fn) real = real/d2 imag = imag/d2 num = (1, 0, im*im) else: num = (0, 0, 1) den = (1, -2*real, real*real + imag*imag) # normalize such that 0 Hz is 0 dB den = np.array(den) gain = den[2]/num[2] den /= gain series += [(num, den)] if n % 2: real = sinh_v0 if type == 2: real = 1/real num = (0, 1) den = (1/-real, 1) series += [(num, den)] return series