Frequency analysis and synthesis of a class of nonlinear filters

Nonlinear filters are analyzed from a spectral point of view. The equivalent frequency behavior of a filter is described by its linear part, which represents the linear nonrecursive filter, that best matches, in the mean-square sense, the behavior of the filter. The class considered includes all the order statistic filters (L-filters) such as median, midrange, alpha-trim, and some new order statistic filters (Ll-filters) defined by the authors to generalize L-filters and FIR filters. The formulation leads to a technique for imposing on the nonlinear filters a given spectral behavior. A simulation of the design for a low-pass Ll-filter is given