Soft saturation

• Author or source: Bram de Jong
• Type: waveshaper
• Created: 2002-01-17 02:18:37

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

• Date: 2005-09-09 21:17:55
• By: gro.esabnaeco@euarg

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!

• Date: 2006-03-12 02:35:16
• By: moc.erawtfosnetpot@nosniborb

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)

• Date: 2006-08-23 06:19:05
• By: moc.liamg@ubibik

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

• Date: 2006-08-24 11:03:04
• By: musicdsp@Nospam dsparsons.co.uk

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