Doctoral thesis:
Automatic Differentiating Wave Digital Filters -
Novel Methods for Convergence Acceleration of Nonlinear Wave Digital Structures and Those containing Delay-Free Loops
Wave digital filters offer a general method for real-time modeling of electrical networks, a concept introduced by Alfred Fettweis in the 1970s. However, not all analog reference circuits can be implemented using this method due to non-computable delay-free directed loops in the resulting signal flow graph, which hinder practical realization. This issue is particularly relevant for circuits with ring-like topologies and nonlinear elements. Iterative methods can resolve these loops, greatly expanding the range of realizable reference networks. The speed of convergence is a critical factor for maintaining real-time capability, and it can vary significantly, especially when choosing artificial port resistances. While the fixed-point iteration method converges linearly, methods like Newton’s and its derivatives offer higher convergence orders but require the function’s derivative at each iteration step during runtime. Automatic differentiation, an algorithmic procedure, provides derivative information for a given function value without needing the function or its derivative to be analytically available. This work explores the application of automatic differentiation to wave digital filters and develops new methods based on these findings.
