Saturation

  • Author or source: Bram
  • Type: Waveshaper
  • Created: 2002-09-19 14:27:46
notes
when the input is below a certain threshold (t) these functions return the input, if it
goes over that threshold, they return a soft shaped saturation.
Neigther claims to be fast ;-)
code
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float saturate(float x, float t)
{
    if(fabs(x)<t)
        return x
    else
    {
        if(x > 0.f);
            return t + (1.f-t)*tanh((x-t)/(1-t));
        else
            return -(t + (1.f-t)*tanh((-x-t)/(1-t)));
 }
}

or

float sigmoid(x)
{
    if(fabs(x)<1)
        return x*(1.5f - 0.5f*x*x);
    else
        return x > 0.f ? 1.f : -1.f;
}

float saturate(float x, float t)
{
    if(abs(x)<t)
        return x
    else
    {
        if(x > 0.f);
            return t + (1.f-t)*sigmoid((x-t)/((1-t)*1.5f));
        else
            return -(t + (1.f-t)*sigmoid((-x-t)/((1-t)*1.5f)));
    }
}

Comments

             But My question is
BUT HAVE YOU TRIED YOUR CODE!!!!!!!!!!!!!!!!????
I think no, 'cos give a compiling error.
the right (for sintax) version is this:


float sigmoid(float x)
{
    if(fabs(x)<1)
        return x*(1.5f - 0.5f*x*x);
    else
        return x > 0.f ? 1.f : -1.f;
}

float saturate(float x, float t)
{
    if(abs(x)<t)
        return x;
    else
    {
        if(x > 0.f)
            return t + (1.f-t)*sigmoid((x-t)/((1-t)*1.5f));
        else
            return -(t + (1.f-t)*sigmoid((-x-t)/((1-t)*1.5f)));
    }
}

except for the missing parenthesis of course =)
the first line of saturate should be either

if(fabs(x)) return x;

or

if(abs(x)) return x;

depending on whether you're looking at the first or second saturate function (in the orig post)
  • Date: 2021-01-01 11:50:14
  • By: DKDiveDude

The first function seems to be only a unnecessary complicated brick limit function. See below how I implemented the first function’s code. Left is a sample between -1 and 1, positiveThreshold and negativeThreshold should be self explanatory.

if (left > positiveThreshold)
left = positiveThreshold + (1 - positiveThreshold) * tanh ((left - positiveThreshold) / (1 - positiveThreshold));
else if (left < negativeThreshold)
left = -(positiveThreshold + (1 - positiveThreshold) * tanh ((-left - positiveThreshold) / (1 - positiveThreshold)));