One-Zero Loop Filter

If we relax the constraint that be odd, then the simplest case becomes the one-zero digital filter:

When , the filter is linear phase, and its phase delay and group delay are equal to sample [371]. In practice, the half-sample delay must be compensated elsewhere in the filtered delay loop, such as in the delay-line interpolation filter [213]. Normalizing the dc gain to unity removes the last degree of freedom so that , and .

See §D.2.3 for related discussion from a software implementation perspective.

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Order a Hardcopy of Physical Audio Signal Processing

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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.