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Practical Advice
In summary, the following pointers can be offered regarding nonlinear
elements in a digital waveguide model:
- Verify that aliasing can be heard and sounds bad before working
to get rid of it.
- Aliasing (bandwidth expansion) is reduced by smoothing
``corners'' in the nonlinearity.
- Consider an oversampling factor for nonlinear
subsystems sufficient to accommodate the bandwidth expansion
caused by the nonlinearity.
- Make sure there is adequate lowpass filtering in a feedback loop
containing a nonlinearity.
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

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).
Another variation is to oversample by two, in which case there
is aliasing, but that aliasing does not reach the ``base band.''
Therefore, a half-band lowpass filter rejects both the second spectral
image and the third, which is aliased onto the second.
Previous: Stability of Nonlinear Feedback LoopsNext: Lumped Models
About the Author: 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.