Systematic Methods for the Implementation of Nonlinear Wave Digital Structures

Wave-digital (WD) structures containing adaptors with memory (characterized by port reflection filters) and nonlinear elements are suitable for the modeling of a wide range of nonlinear circuits and physical structures. In this paper, we propose two methods for automating the construction of algorithms that efficiently implement such structures, starting from their symbolic description. The former is based on the solution of state-space equations, while the latter is based on direct structural inspection. The state-space approach starts from the blockwise construction of a tableau matrix for the direct implementation of a generic WD structure and, for this reason, is here referred to as the wave tableau (WT) method. It has very general applicability as it works for a generic WD structure. The second technique (binary connection tree) implements a WD structure through a direct inspection (scanning) of the treelike topological representation of the reference model. Although valid for a slightly less general range of cases, this approach turns out to be much more efficient and flexible than that of the WT method. Such methods are particularly interesting for an interactive and immediate prototyping of physical models for the synthesis of sounds as they bring nonlinear WD structures with dynamic adaptors to a level of practical usability for a wide range of users while enabling the modeling of a wide variety of time-varying nonlinear physical models in an automatic fashion. The proposed solutions have been extensively tested on applications for the automatic modeling of acoustic interactions of musical interest.