Biparametric Wave Digital Filters

We propose a novel class of wave digital filters (WDFs), called Biparametric WDFs (BWDFs), whose power-normalized waves are defined as having two free parameters instead of just one. We explore the advantages brought by this generalization by first deriving the scattering relations and the corresponding adaptation conditions for the most common circuit elements. We then show that the added free parameters allow us to define adaptors whose ports can all be simultaneously adapted; and that these adaptors are reciprocal and their scattering relations can be defined to be multiplierless and independent of the circuit parameters. We also show that the computational cost and memory requirements of BWDFs turn out to be reduced with respect to traditional WDFs based on power-normalized waves. We then discuss the impact of this generalization on the ability of wave digital structures of this sort to accommodate nonlinear elements. We finally develop explicit wave mappings for nonlinear diodes, and discuss some examples of applications to specific nonlinear circuits (i.e., an envelope detector, an unbiased double diode clipper, and a biased double diode clipper).