Sign in

username:

password:



Not a member?

Search Online Books



Search tips

Free Online Books

Sponsor

NEW! TMS320C6474: 3x the performance. 1/3 the cost. Three 1 GHz cores on 1 chip.

Chapters

Chapter Contents:

Search Physical Audio Signal Processing

  

Book Index | Global Index


Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?

  

Practical Advice

To summarize this appendix, the following pointers can be offered:

  • 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 using an oversampling factor for nonlinear subsystems that is 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 §4.13). 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 lowpass filter and upsample by 3 just before 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 (see §K.3).

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.


Order a Hardcopy of Physical Audio Signal Processing

Previous: Cubic Soft-Clipper
Next: Resources on the Internet

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 Researc