Digital Waveguide Networks

A Digital Waveguide Network (DWN) consists of any number of digital waveguides interconnected by scattering junctions. For example, when two digital waveguides are connected together at their endpoints, we obtain a two-port scattering junction as shown in Fig.2.33. When three or more waveguides are connected at a point, we obtain a multiport scattering junction, as discussed in §C.8. In other words, a digital waveguide network is formed whenever digital waveguides having arbitrary wave impedances are interconnected. Since DWNs are lossless, they provide a systematic means of building a very large class of MIMO allpass filters.

Consider the following question:

Under what conditions may I feed a signal from one point inside a given allpass filter to some other point (adding them) without altering signal energy at any frequency?

In other words, how do we add feedback paths anywhere and everywhere, thereby maximizing the richness of the recursive feedback structure, while maintaining an overall allpass structure?

The digital waveguide approach to allpass design [430] answers this question by maintaining a physical interpretation for all delay elements in the system. Allpass filters are made out of lossless digital waveguides arranged in closed, energy conserving networks. See Appendix C for further discussion.

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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.