A multidimensional approach to Wave Digital Filters with multiple nonlinearities

The implementation of nonlinear elements in Wave Digital Filters (WDFs) is usually restricted to just one nonlinear one-port per structure. Existing approaches that aim to circumvent this restriction have in common that they neglect the notion of modularity and thus the reusability of the original Wave Digital concept. In this paper, a new modular approach to implement an arbitrary number of nonlinearities based on Multidimensional Wave Digital Filters (MDWDFs) is presented. For this, the contractivity property of WDFs is shown. On that basis, the new approach is studied with respect to possible side-effects and an appropriate modification is proposed that counteracts these effects and significantly improves the convergence behaviour.