A multidimensional signal processing approach to Wave Digital Filters with topology-related delay-free loops

To avoid the occurrence of noncomputable, delay-free loops, classic Wave Digital Filters (WDFs) usually exhibit a tree-like topology. For the realization of prototype circuits that contain ring-like subnetworks, prior approaches require the decomposition of the structure and thus neglect the notion of modularity of the original Wave Digital concept. In this paper, a new modular approach 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.