Chebyshev Distortion

cheb_distortion.py

import numpy as np

def cheb(n,x):
    if(n == 1): return x
    if(n == 0): return 1
    else: return 2*x*cheb(n-1, x) - cheb(n-2, x)


def add_cheb_distortion(signal, n, ampl = lambda x: 1):
    squash = lambda x,k,L,A: (L-A)/(1+np.exp(k*x))
    output = np.zeros_like(signal)
    for i in range(0,4):
        output += ampl(i) * cheb(i, inSig)
    return squash(output,-2, 40, 0)

Chebyshev Polynomials have deep relationships with pure harmonics.

This algorithim is an implementation of A Tutorial on Non-Linear Distortion or Waveshaping Synthesis by C.Roads published in Computer Music Journal Vol. 3, No. 2 (Jun., 1979).