Hi community,

Trying to create a waveshaper using a sigmoid transfer function. Have read miller puckette's book and looked at the examples, but can't seem to get to grips with how to get my sigmoid function to write to an array.

The function i'm looking to use as my waveshaper is:

F(f)=h+k tanh⁡(f)

Attached is a graphical version.

Any help would be great!

http://www.pdpatchrepo.info/hurleur/Screen_shot_2013-07-10_at_16.53.53.png

you might not even need an array. tanh is pretty simple. actually, there's an external that does it (tanh~)

or you can use this 'cheap' approximation that i ripped from somewhere (sorry, i forgot where!)

(and to increase the steepness, you just need to multiply the original signal by a factor of 1 to 3)

http://www.pdpatchrepo.info/hurleur/diytanh~.pd

by the way, you're on the right track with this. tanh is pretty much THE most useful function for natural sounding synths and effects.

I have several in almost everything i make.

Hi mod, thanks for the swift reply!

Here's my sigmoid transfer function for the equation written in my first post. Maybe i'm missing something, but I can't seem to get it to work properly. It just seems to move the waveform up and down by the factor of H which says to me the tanh isn't functioning. It's probably something very elementary, but i've got myself in a muddle trying to work it out through looking at other examples and now i'm a little lost with it.

http://www.pdpatchrepo.info/hurleur/sigmoid.pd

you're adding a dc value? what are you implementing? the equation and the picture in your first post are very different
...maybe multiply and add before passing to the tanh?
as a side note the [*~] and [+~] family of objects are more efficient with a control inlet as a second inlet (you can do this by passing them arguments at creation)

I'm using this transfer function within a flute waveguide. Here's the excerpt about the transfer function.

"where f is the value of the volume flow advancing towards the
embouchure hole, k is a gain term, and h describes the deviation
of the center line of the air jet from the wedge. By changing the value of h it is possible to produce asymmetrical wavefom or- in other words - sounds that also have even harmonics in their spectrum. When h is zero, the spectrum of the output of the model has very weak even harmonics"

Admittedly the following excerpt is about another slightly different function (see screenshot), but the idea is still the same.

f(x) = -1 if x<= -1.325
x^3-x if 1.325<x<-1.325
1 if x>=1.325

"If the input signal does not go beyond (-1.325,1.325) range the waveshaper inverts the phase of the input signal and introduces a third harmonic. Once the range is exceeded, hard limiting occurs and inserts odd harmonics from clipping."

http://www.pdpatchrepo.info/hurleur/Screen_shot_2013-07-12_at_10.31.44.png

I'm guessing that this implementation is completely correct within the waveguide. The first screenshot you posted is just the part going into the tanh, but you are adding h to the function so of course the whole thing will be translated vertically. if you add gain before going into the tanh it will look like the screenshot, which is what will probably happen in the waveguide.