Wave Digital Filter Models

Perhaps the best known physics-based approach to digital filter design is wave digital filters, developed principally by Alfred Fettweis [136].^A.9Wave digital filters may be constructed by applying the bilinear transform [343] to the scattering-theoretic formulation of lumped RLC networks introduced in circuit theory by Vitold Belevitch [34]. Fettweis in fact worked with Belevitch.^A.10Scattering theory had been in use for many years prior in quantum mechanics.

A key, driving property of wave digital filters is low sensitivity to coefficient round-off error. This follows from the correspondence to passive circuit networks. Wave digital filters also have the nice property of preserving order of the original (analog) system. For example, a ``wave digital spring'' is simply a unit delay, and a ``wave digital mass'' is a unit delay with a sign flip. The only approximation aspect is the frequency-warping caused by the bilinear transform. It is interesting to note that when it is possible to frequency-warp input/output signals exactly, a wave digital filter can implement a continuous-time LTI system exactly! See [55] for a discussion of wave digital filters and their relation to finite differences et al.

In computer music, various ``wave digital elements'' have been proposed, including wave digital toneholes [527], piano hammers [56], and woodwind bores [525].

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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.