Create distortion from basic linear (and non-linear if neccessary) DSP elements

Question

I'm studying mechatronics and I'm intrested in DSP basics. My lecturer said that there are four basic linear DSP elements:

1. Adder (and other mathematical operations)
2. Amplification (shown on diagrams as triangle)
3. Delay ($z^{-1}$)
4. Junction

I know from electronics that I can create distortion using for example op-amps and clipping circuits - and I can do it practically. But is there a way to create distortion using four DSP elements theoretically? I know distortion is non-linear - so if not this four elements, what kind of elements existing in theoretically DSP should i use?

Answer 1

Using those four basic elements will allow you to implement linear systems, which can change the magnitude and phase of the input signal, but which will not add the harmonics that are expected from a distortion effect. In order to create distortion in that sense (i.e., non-linear distortion) you will need some non-linear element. The most basic implementation would use a (soft) clipping function, possibly followed by some linear filter to shape the spectrum.

A very accessible reference is the DAFX (Digital Audio Effects) book edited by Udo Zölzer. It has a chapter on non-linear processing, including distortion and overdrive. Note that I found an error in one of the equations for producing distortion (Eq. (5.9)). You can find the corrected formula in this answer to a related question.