Multiband Distortion

While the cubic nonlinearity described in § gives plausible results, higher quality may be obtained through the use of oversampling and frequency-dependent pre- and post-distortion gains.^D.11

Amp =
F1: one or two biquads
S: saturating nonlinearity
F2: one or two biquads

Let F1 = highpass ~ differentiator
Upsample (e.g. 8x [e.g., Line 6 patent] or 4x)
S limits derivative
Result: slew-rate limiter
Use extra-low cutoff frequency
Downsample
F1 = biquad parametric = emphasis filter => which frequencies get clipped
S: hard to soft limiting - JSA likes x/(1+|x|^n)^(1/n)
   => linear at small x, x/|x|
   n around 2 or 3 is like arctan = back-to-back diodes case
   n 4 or 5 gives sharper corner
   High input gain gives more clipping

F2: Eq filter
   1/F1 + whatever equalization
   Can bandlimit some of the distortion
   Can be a parametric, but a parametric + shelf is nice

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.