Efficient computation of nonlinear filter networks with delay-free loops and applications to physically-based sound models

The paper presents a general procedure for the computation of filter networks made of linear filters and non-linear non-algebraic (dynamic) elements. The method is developed in the Kirchhoff domain and applies to cases where the network contains an arbitrary number of delay-free paths that involve nonlinear elements. Compared to existing techniques the method does not require a rearrangement of the network structure, instead it subdivides the network into computational substructures specified by appropriate matrices related to the network topology. Sufficient conditions are discussed for the applicability of the method, and results are provided that relate performance of the method to the properties of the nonlinear elements and to the network topology. The last part of the paper discusses applications of the method to the simulation of acoustic systems, including multidimensional wave propagation by means of waveguide-mesh techniques.