Wave Digital Filters

Wave digital elements may be derived as follows:

1. Express forces and velocities as sums of traveling-wave components (``wave variables''):
   $$\begin{eqnarray*} f(t) &=& f^{{+}}(t)+f^{{-}}(t)\\ v(t) &=& v^{+}(t)+v^{-}(t) \end{eqnarray*}$$
   

   The actual ``travel time'' is always zero.

2. Digitize via the bilinear transform (trapezoid rule)

3. Use scattering junctions (``adaptors'') to connect elements together in series and/or parallel.