Canonical Piecewise-Linear Representation of Curves in the Wave Digital Domain

Global, explicit representations of nonlinearities are desirable when implementing nonlinear Wave Digital (WD) structures, as they free us from the burden of managing look-up tables, performing data interpolation and/or using iterative solvers. In this paper we present a method that, starting from certain parameterized PieceWise-Linear (PWL) curves in the Kirchhoff domain, allows us to express them in the WD domain using a global and explicit representation. We will show how some curves (multi-valued functions in the Kirchhoff domain) can be represented as functions in canonical PWL form in the WD domain. In particular, we will present a procedure, which, in the most general case, also returns the conditions on the reference port resistance under which it is possible to find explicit mappings in the WD domain.