[PD] Guitar distortion (Chebyshev?)

Mathieu Bouchard matju at artengine.ca
Mon Sep 13 17:40:11 CEST 2010


On Sun, 12 Sep 2010, Martin Peach wrote:

>> plot [-2:2] [-1:1] exp(x*sqrt(2))-1, 1-exp(-x*sqrt(2)), tanh(x), x
> Of course, all the hyperbolic trig functions are made from exp, by 
> definition.

Ah, some other things I wanted to say :

Even though tanh is made from exp, it's not directly the same as the two 
simpler exponentials (above) that may describe capacitor behaviour more 
directly. What I wanted to show is tanh is a rather good approximation to 
both at once, but only if you put an extra sqrt(2) factor.

And to finish about the sigmoïd, tanh(x) is usually written as 
(exp(x)-exp(-x))/(exp(x)+exp(-x)), but you can also write it as 
1-2/(1+exp(2*x)), which is almost the usual form of the sigmoïd function.

  _______________________________________________________________________
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC


More information about the Pd-list mailing list