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Newton's method for modularity-preserving multidimensional wave digital filters

Wave Digital Filter (WDF) theory provides an immediate method to derive robust, stable and real-time capable discretizations of one- or multidimensional prototype networks. However, there are realization constraints for certain types of structures, e.g. the presence of multiple nonlinearities, which result in non-computable implicit relations. A common approach to circumvent this restriction is wave-based modeling with state-space-like structures, where implicit equations are solved iteratively by Newton's method or similar approaches. Unfortunately, these concepts generally give up the modular structure of the WDF, thus the reusability, extendability and topology of the prototype network. In this paper, two multidimensional iteration methods based on Newton's method are proposed that are strictly modular and fit well into the modular concept of WDFs.