[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
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