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Wave Digital Filters

A Wave Digital Filter (WDF) [127] is a particular kind of digital filter based on physical modeling principles. Unlike most digital filter types, every delay element in a WDF can be interpreted physically as holding the current state of a mass or spring (or capacitor or inductor). WDFs can also be viewed as a particular kind of finite difference scheme having unusually good numerical properties [50]. (See Appendix L for an introduction to finite difference schemes.)

Wave digital filters were developed initially by Alfred Fettweis [125] in the late 1960s for digitizing lumped electrical circuits composed of inductors, capacitors, resistors, transformers, gyrators, circulators, and other elements of classical network theory [127]. The WDF approach is based on the traveling-wave formulation of lumped electrical elements introduced by Belevitch [32], and derived in §J.6.

A WDF is constructed by interconnecting simple discrete-time models of individual masses, springs, and dashpots (or inductors, capacitors, and resistors). The rules for interconnecting the elementary models are based on scattering theory (discussed in §G.8). This is a direct result of the fact that all signals explicitly computed may be physically interpreted as traveling wave components of physical variables.



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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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