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Wave Digital Filters

Perhaps the best known physics-based approach to digital filter design is wave digital filters, developed principally by Alfred Fettweis [127].D.9Wave digital filters may be constructed by applying the bilinear transform [323] to the scattering-theoretic formulation of lumped RLC networks introduced in circuit theory by Vitold Belevitch [32]. Fettweis in fact worked with Belevitch.D.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 [50] 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 [497], piano hammers [51], and woodwind bores [495].


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[How to cite and copy this work] 
``Physical Audio Signal Processing for Virtual Musical Instruments and Digital Audio Effects'', by Julius O. Smith III, (December 2005 Edition).
Copyright © 2006-07-01 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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