tanh.py

# ref.: https://www.kvraudio.com/forum/viewtopic.php?t=388650&start=45
# original.: https://nbviewer.jupyter.org/gist/JTriggerFish/6226363
# added fast tanh of JUCE library

from numpy import *
import scipy as sp
from scipy import signal
import matplotlib.pyplot as plt
%matplotlib inline
import matplotlib
#matplotlib.rcParams['savefig.dpi'] = 1 * matplotlib.rcParams['savefig.dpi']
matplotlib.rcParams['figure.figsize'] = (20,5)

N=4096
factor=1

f = 1./7.8

t = linspace(0, N, N)
freq = fft.fftfreq(N*factor, t.shape[-1])

sine = sin(2*pi*f*t)
saw  = sp.signal.sawtooth(2*pi*f*t)

def showAbsFFT(signal):
    window = blackman(N)
    windowed = window*signal
    padded   = pad(windowed, (0, N*factor - N), 'constant', constant_values=(0))
    signalX = fft.fft(padded) / N
    amplX = abs(signalX)
    plt.plot(freq[0:int(len(padded)/2)], 20*log(amplX)[0:int(len(padded)/2)])
    
showAbsFFT(sine)

def vox_fasttanh_ultra(X):
   ax = fabs( X ); 
   x2 = X * X; 
   Z = X * ( 0.773062670268356 + ax + 
      ( 0.757118539838817 + 0.0139332362248817 * x2 * x2 ) * 
      x2 * ax ); 

   return( Z / ( 0.795956503022967 + fabs( Z )))

def vox_fasttanh2( x ): 
   ax = fabs( x ); 
   x2 = x * x; 

   return( x * ( 2.45550750702956 + 2.45550750702956 * ax + 
      ( 0.893229853513558 + 0.821226666969744 * ax ) * x2 ) / 
      ( 2.44506634652299 + ( 2.44506634652299 + x2 ) * 
      fabs( x + 0.814642734961073 * x * ax ))); 

def juce_tanh( x ):
    x2 = x * x;
    numerator = x * (-135135 + x2 * (17325 + x2 * (-378 + x2)));
    denominator = -135135 + x2 * (62370 + x2 * (-3150 + 28 * x2));
    return numerator / denominator;

showAbsFFT(tanh(sine))
showAbsFFT(vox_fasttanh_ultra(sine))
showAbsFFT(vox_fasttanh2(sine))
showAbsFFT(juce_tanh(sine))