A recursive variant of Mallows' filter class

Mallows' nonlinear FIR filter class includes most of the nonlinear digital filters in wide use today. This filter class is defined in terms of five ax ioms, and this paper modifies two of these axioms to obtain a class of symm etric recursive nonlinear filters. One of the main points considered in thi s paper is the consequence of Mallows' location invariance axiom A2, and ge neral prescriptions are given for both Mallows' original FIR filter class a nd its recursive extension. This representation is also extremely useful in dicussing the root sequences of both the recursive and nonrecursive struct ures. Since recursive filters can exhibit various forms of instability, a n umber of stability results are presented for this class of filters. Finally , some simple examples are considered that illustrate the potential utility of the results presented here.