Waveshaping
Waveshaping
Non-linear amplitude processing
scaling the amplitude according to a waveshaping function
Roads. Computer Music Tutorial
Like FM is an economical method of synthesizing complex spectra
image from
audiomulch.com > Blog > Illuminating-shaper-contraption
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.
From Dodge, Jerse. Computer Music: Synthesis, Composition and Performance.
Sensitive to amplitude
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
Otherwise the output amplitude might be too inconsistent
This can be done at the output through peak or power matching
Classic waveshaping synthesis
waveshaping function is a Chebyshev polynomial of the first kind
T_0(x) = 1
T_1(x) = x
T_2(x) = 2x^2-1
T_3(x) = 4x^3-3x
T_4(x) = 8x^4-8x^2+ 1
T_5(x) = 16x^5-20x^3+5x
T_6(x) = 32x^6-48x^4+18x^2-1
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
Also used frequently to produce disortion
with a tanh function for example
Quantization distortion using a stepped waveshaping function
or controlling the size of the shaper function