Wave Digital Filters

A Wave Digital Filter (WDF) [137] 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 [55]. (See Appendix D for an introduction to finite difference schemes.) WDFs have been applied often in music signal processing [397,341,559,364,351,560,558,56,531,527,487].

Wave digital filters were developed initially by Alfred Fettweis [136] in the late 1960s for digitizing lumped electrical circuits composed of inductors, capacitors, resistors, transformers, gyrators, circulators, and other elements of classical network theory [137]. The WDF approach is based on the traveling-wave formulation of lumped electrical elements introduced by Belevitch [34].

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 §C.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.