Toward the Wave Digital Real-Time Emulation of Audio Circuits with Multiple Nonlinearities

Over the past two decades, Wave Digital Filters have been extensively used in the fields of sound synthesis through physical modeling and Virtual Analog modeling to emulate audio circuits in an efficient and modular fashion. However, as far as the implementation of circuits with multiple nonlinearities is concerned, much research effort is still needed in order to develop systematic strategies for solving the corresponding multivariate systems of implicit equations with low computational requirements. In this regard, this paper discusses the computational cost of the Scattering Iterative Method (SIM), a recently proposed iterative fixed-point algorithm that works in the Wave Digital domain and it is capable of handling circuits with J one-port nonlinearities using J separate local solvers. In the light of the computational cost analysis, we also propose a refinement of SIM relying on the so called Dynamic Scattering Matrix Recomputation (DSR) procedure. The DSR procedure significantly improves the performance of the algorithm, paving the way toward Virtual Analog applications in which SIM-based audio plugins emulating nonlinear circuits run in real-time.