Mathematics in distortion effects

Special Interest Groups Audio Processing
1

I have use the dsitoration effects in audacity, sounds pretty good. And I am very interested in “Cubic Curve (odd harmonics)” and “Expand and Compress”.
Can anyone help explain the principle of implementation in it? Or recommend some related information notes.
Thanks.

2

Audacity’s “Distortion” effect is a “waveshaper”.

Basically it maps sample values to new values depending on the value. For example, the “hard clipping” setting in pseudo code:

IF
    sample_value > positive_threshold
THEN
    sample_value = positive_threshold
ELSE IF
    sample_value < negative_threshold
THEN
    sample_value = negative_threshold
ELSE
    PASS  # use the original sample value

Notes:

  • As a point of interest, Audacity’s Distortion effect was originally implemented in Nyquist, using the SHAPE function.
  • Cubic formula: y = x - (x^3 / 3.0)
3

Cubic distortion generating odd (not even) harmonic (3kHz) …
toolchain

Now the bad news: in Audcaity3 if you try to insert text into a plugin,
(e.g. math formula or hex serial-number), some letters are do not appear,
and instead are misinterpreted by Audacity as keyboard shortcuts.

4

Is that a new / known issue?

5

This looks similar … Label loses focus when typing on Mac OS Ventura · Issue #3883 · audacity/audacity · GitHub
[ I’m getting it on Windows ].

7

Thanks for your reply.

8

This comes from “[sin(x)]^3 = 3/4sin(x) - 1/4sin(3x)” ?
if x = sin(x),
y = 3/4sin(x) + 1/12sin(3x)

9

toolchain-abc

NB: This Toolchain plugin does not work reliably in Audacity.