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Soft saturation

Type : waveshaper
References : Posted by Bram de Jong

Notes :
This only works for positive values of x. a should be in the range 0..1

Code :
x < a:
f(x) = x
x > a:
f(x) = a + (x-a)/(1+((x-a)/(1-a))^2)
x > 1:
f(x) = (a+1)/2



Comments


Added on : 09/09/05 by graue[ AT ]oceanbase[ DOT ]org
Comment :
This is a most excellent waveshaper.

I have implemented it as an effect for the music tracker Psycle, and so far I am very pleased with the results. Thanks for sharing this knowledge, Bram!




Added on : 11/03/06 by brobinson[ AT ]toptensoftware[ DOT ]com
Comment :
I'm wondering about the >1 condition here.  If a is 0.8, values <1 approach 0.85 but values >1 are clamped to 0.9  (there's a gap)

If you substitute x=1 to the equation for x>a you get: a+((1-a)/4) not (a+1)/2

Have I missed something or is there a reason for this?

(Go easy I'm new to all of this)




Added on : 23/08/06 by kibibu[ AT ]gmail[ DOT ]com
Comment :
Substituting x=1 into equation 2 (taking many steps)

f(x) = a + (x-a)/(1+ ((x-a)/(1-a))^2)
     = a + (1-a)/(1+ ((1-a)/(1-a))^2)
     = a + (1-a)/(1+ 1^2)
     = a + (1-a)/2
     = 2a/2 + (1-a)/2
     = (2a + 1 - a) /2
     = (a+1) / 2




Added on : 24/08/06 by musicdsp[at] Nospam dsparsons[dot]co[dot]uk
Comment :
You can normalise the output:
f(x)'=f(x)*(1/((a+1)/2))

This gives a nice variable shaper with smooth curve upto clipping at 0dBFS




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