Waveshaping

Roads. Computer Music Tutorial

image from

A function symmetrical around the origin will generate only odd harmonics; one that is symmetrical around the vertical axis will only produce even harmonics. Jagged functions may cause aliasing.

Non-linear, so the same signal at different amplitude will produce a different output

For this reason it can simulate the way real instruments work, but having a wavashaping function that produces brighter spectra for higher amplitudes

Becase the output amplitude depends on the waveshaping function, the output amplitude must be adjusted

waveshaping function is a Chebyshev polynomial of the first kind

Source is a cosine oscillation

The output is a predictable harmonic spectrum

Using Chebyshev polynomials in the range [-1, 1] ensures that the resulting waveform is band limited

with a tanh function for example

Quantization distortion using a stepped waveshaping function