pole.py

import mpmath as mp

def butterworth(n):
    '''Returns a list of Q,f multiplier values for a cascade of length N.'''

    n = int(n)
    step = mp.pi/(2.0*n)
    start = step/2.0

    q = []
    value = start
    while value < mp.pi/2:
        q.append(1./(2.0*mp.cos(value)))
        value += step

    return q, [1.0] * int(n)


# Presolved bessel Q,f (a,b) polynomials
BESSEL_Q = [
    [0.57735026919],
    [0.805538281842, 0.521934581669],
    [1.02331395383,  0.611194546878, 0.510317824749],
    [1.22566942541,  0.710852074442, 0.559609164796, 0.505991069397],
    [1.41530886916,  0.809790964842, 0.620470155556, 0.537552151325, 0.503912727276],
    [1.59465693507,  0.905947107025, 0.684008068137, 0.579367238641, 0.525936202016, 0.502755558204],
    [1.76552743493,  0.998998442993, 0.747625068271, 0.624777082395, 0.556680772868, 0.519027293158, 0.502045428643],
    [1.9292718407,   1.08906376917,  0.810410302962, 0.671382379377, 0.591144659703, 0.542678365981, 0.514570953471, 0.501578400482]
]

BESSEL_F = [
    [1.0],
    [1.05881751607, 0.944449808226],
    [1.10221694805, 0.977488555538, 0.928156550439],
    [1.13294518316, 1.01102810214, 0.948341760923, 0.920583104484],
    [1.1558037036, 1.03936894925, 0.972611094341, 0.934100034374, 0.916249124617],
    [1.17355271619, 1.06292406317, 0.99546178686, 0.952166527388, 0.92591429605, 0.913454385093],
    [1.18780032771, 1.08266791426, 1.0159112847, 0.970477661528, 0.939810654318, 0.920703208467, 0.911506866227],
    [1.19953740587, 1.09943305993, 1.03400291299, 0.987760087301, 0.954673832805, 0.93169889496, 0.917142770586, 0.910073839264]
]

def bessel(n):
    '''Returns a list of Q,f multiplier values for a cascade of length N.'''

    n = int(n)

    if n > 8:
        print("Max cascade length for Bessel filters is 8")
        exit(1)

    # Return with smallest Q in the first stage
    return BESSEL_Q[n-1][::-1], BESSEL_F[n-1][::-1]