Homogeneous nonlinear digital filters

Linearity may be defined behaviorally via the well-known principle of superposition. This paper describes three useful relaxations of the principle of superposition, all of which lead to interesting classes of nonlinear digital filters: homogeneity, positive-homogeneity, and static-linearity. In fact, many popular digital filters fall into these classes and this paper explores the use of these characterizations in the analysis and design of nonlinear filters. Complete characterizations of the FIR subclass are given for two of these nonlinear filter classes, and useful closure properties are presented which provide a basis for constructing more general (e.g., recursive) members of all three of these filter classes. These ideas are used to develop a recursive modification of the standard median filter.