Wave Digital Filter Models

Perhaps the best known physics-based approach to digital filter design
is *wave digital filters*, developed principally by Alfred
Fettweis [137].^{A.9}Wave digital filters may be constructed by applying the bilinear
transform [346] to the scattering-theoretic
formulation of lumped RLC networks introduced in circuit theory by
Vitold Belevitch [34]. Fettweis in fact worked with
Belevitch.^{A.10}Scattering 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 [531], piano hammers [56], and woodwind bores [529].

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