Wave digital filters (WDF) were initially developed by Alfred Fettweis in the late 1960s for digitizing lumped electrical circuits.
Wave digital filter techniques involve the use of traveling-wave variables in the context of lumped system analysis.
Very simple expressions can be developed for various physical components, such as masses, springs, and dashpots. These components can then be interconnected using adaptors, which are scattering junction interfaces.
WDF techniques are convenient when trying to eliminate delay-free loops because of the flexibility available in defining system wave impedances.
A WDF model of a system can be developed from its continuous-time, differential equation representation as follows:
Express all physical quantities, such as forces and velocities, in terms of traveling-wave components.
Digitize the resulting traveling-wave system using the bilinear transform.
Combine elementary components (mass, springs, ...) using scattering junctions defined by either series or parallel connections.
For a more detailed and complete discussion, see the following wave digital filter
link.