Advances in Wave Digital Modeling of Linear and Nonlinear Systems: A Summary

Abstract

This brief summarizes some of the main research results that I obtained during the three years, ranging from November 2015 to October 2018, as a Ph.D. student at Politecnico di Milano under the supervision of Professor Augusto Sarti, and that are contained in my doctoral dissertation, entitled "Advances in Wave Digital Modeling of Linear and Nonlinear Systems". The thesis provides contributions to all the main aspects of Wave Digital (WD) modeling of lumped systems: it introduces generalized definitions of wave variables; it presents novel WD models of one-and multi-port linear and nonlinear circuit elements; it discusses systematic techniques for the WD implementation of arbitrary connection networks and it describes a novel iterative method for the implementation of circuits with multiple nonlinear elements. Though WD methods usually focus on the discrete-time implementation of analog audio circuits; the methodologies addressed in the thesis are general enough as to be applicable to whatever system that can be described by an equivalent electric circuit.

Non-Iterative Simulation Methods for Virtual Analog Modelling

“…Discretetime algorithm design is governed by a number of problems: these include achieving reasonable accuracy, computational efficiency, and the ensuring of robust (numerically stable) behaviour. Various virtual analog (VA) modeling frameworks have emerged, including state-space models (SSMs) [1], [2], [3], Port-Hamiltonian Systems (PHSs) [4], [5], and Wave Digital Filters (WDFs) [6], [7], [8].…”