Optimization of Artificial Port Reflectances for Wave Digital Filters with Topology-Related Delay-Free Loops

In this paper, a generic method for fast determination of all involved optimal artificial port resistances is presented for the realization of Wave Digital Filters (WDFs) containing noncomputable, delay-free loops. Therefore, the concept of Automatic Differentiating WDFs (ADWDFs) is applied to obtain said resistances by minimizing the associated artificial reflectances, which performs significantly faster than empirical approaches, as will be shown in an example. This way, the resulting Wave Digital structure remains completely modular under fixed point iteration schemes achieving optimal convergence speeds. Additionally, contractivity of WDFs is exploited to obtain an optimal operating point from a different perspective.