Wave digital filters with multiple nonlinearities

The wave digital filter (WDF) theory provides an elegant method for the discretization of linear continuous filters which is well known for possessing many desirable properties over other filter implementations. However, concerning nonlinear networks so far there are only solutions for circuits with a single nonlinearity, as the delay-free-feedback of the nonlinear element may result in delay-free-loops for multiple nonlinearities. In this paper we present a method to circumvent this problem by the introduction of a vector-nonlinearity. We show how to incorporate multiple nonlinear elements in a WDF structure and how to implement this method using the look-up-tables of the nonlinearities. This method of implementation is demonstrated for the scalar case by the well known Chua's circuit and for the vector case by a circuit with two real diodes.