Toward nonlinear wave digital filters

The wave digital filter (WDF) theory provides us with a systematic methodology for building digital models of analog filters through the discretization of their individual circuit components. In some situations, WDF principles can also be successfully used for modeling circuits in which a nonlinear circuit element is present under mild conditions on its characteristic. In this paper, we propose an extension of the classic WDF principles, which allows us to considerably extend the class of nonlinear elements that can be modeled in the wave digital domain. The method we propose is based on a new class of waves that can be chosen in such a way that incorporates the intrinsic dynamics of a nonlinear element into a new class of dynamic multiport adaptors. This family of junctions represents a generalization of the concept of “mutator” in the analog nonlinear circuit theory because it allows us to treat a nonlinear dynamic element as if it were instantaneous (resistive).