Half-Rate Waveguide Filters

The delays preceding the two inputs to a junction can be ``pushed'' into the junction so that they emerge on the outputs and combine with the delays there. (This is easy to show using the Kelly-Lochbaum scattering junction derived in §H.8.4.) By performing this operation on every other section in the DWF chain, the filter structure of Fig.I.2 is obtained. This structure has some advantages worth considering: (1) it consolidates delays to length as do conventional lattice/ladder structures, (2) it does not require a termination by an infinite wave impedance, allowing it to be extended to networks of arbitrary topology (e.g., multiport branching, intersection, and looping), and (3) there is no long delay-free signal path along the upper rail as in conventional lattice/ladder structures--a pipeline segment is only two sections long. This structure appears to have better overall characteristics than any other digital filter structure for many applications. Advantage (2) makes it especially valuable for modeling physical systems.

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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.