Wave Digital Filters

Wave digital filters were originally conceived as a way of discretizing an analog filter containing resistors, capacitors, inductors, transformers etc.

An alternative view would be that we are numerically integrating the set of ODEs which describes the analog circuit. Consider again the case of an inductor, which we will again discretize by the trapezoid rule for numerical integration (equivalent to the bilinear transform $s$-plane to $z$-plane mapping):