Distortion

The distortion effect lowers the clipping roof of the signal. This causes the tone to sound more "fuzzy" of "gritty". There are 2 main ways of handling this process: Hard Clipping and Soft Clipping

Hard Clipping

Hard clipping cuts the signal to the clipping roof. This results in the wave having a very harsh cut. This results in the distortion sounding more aggressive and gritty.

Soft Clipping

Soft clipping smoothes the transition to the roof so that the wave isn't cut off. This give the audio a more warm and compressed sound.

The function we use to smooth out the signal is defined as:

$$f(x)=\frac{x}{(1+|x|^n)^{\frac{1}{n}}}$$

Where $f(x)$ is the output or wet sample, $x$ is the ingoing/dry sample and $n$ is the smoothness parameter set between 1 and 10. 1 being maximum smoothing and 10 minimal. If we don't limit $n$, then $n \rightarrow \infty$ would create Hard Clipping Distortion.

Because this function smoothed towards -1 and 1, we need to normalize the ingoing sample by dividing it by the configurable clipping limit and denormalizing the outgoing sample to get back to the desired amplitude.