A Wave Digital Filter (WDF)  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 . (See Appendix D for an introduction to finite difference schemes.) WDFs have been applied often in music signal processing [397,341,557,364,351,558,556,56,529,525,486].
Wave digital filters were developed initially by Alfred Fettweis  in the late 1960s for digitizing lumped electrical circuits composed of inductors, capacitors, resistors, transformers, gyrators, circulators, and other elements of classical network theory . The WDF approach is based on the traveling-wave formulation of lumped electrical elements introduced by Belevitch .
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.