An Improved Multi-Dimensional Approach to Wave Digital Filters with Topology-Related Delay-Free Loops using Automatic Differentiation

To avoid the occurrence of non-computable, delay-free loops, classic Wave Digital Filters (WDFs) usually exhibit a tree-like topology. However, recent advances led to a strictly modular realization of the former structures by identification of contractivity properties of WDFs, allowing an assured converging iterative procedure, which depends on the presence of artificial port resistances. In this paper, an improved semi-modular approach based on Multi-dimensional Wave Digital Filters (MDWDFs) is presented for the mentioned topologies. Therefore, a new method of Automatic Differentiating Wave Digital Filters (ADWDFs) is proposed to overcome convergence speed limitations induced by artificial port resistances, making the improved approach independent of the same.