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Chebyshev Distortion
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| 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) |
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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).