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Practical Advice

In summary, the following pointers can be offered regarding nonlinear elements in a digital waveguide model:

As a specific example, consider the cubic nonlinearity used in a feedback loop (as in §9.1.6). This can be done with no aliasing at low levels (i.e., at levels below hard clipping) provided we use To avoid $ 3\times$ oversampling in the entire feedback loop, we may downsample by 3 after the lowpass filter and upsample by 3 just before the nonlinearity. If the lowpass filter is good, the downsampling by 3 is trivially accomplished by throwing away every 2 out of 3 samples. For upsampling, however, an additional third-band lowpass-filter is needed for the interpolation (§4.4).

A more agressive antialiasing scheme is to oversample by only two (or between 2 and 3) for cubic nonlinearities, in which case there is aliasing in the transition band, but it does not reach the passband. More generally, for an $ N$ th-order nonlinearity, oversampling by $ N/2$ suffices to keep aliasing out of the passband. This is a reasonable choice when the passband is the full audio band, or (using a bit more oversampling) when the lowpass filter is high order.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2023-08-20 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University