Generalized order statistic filters

The authors explore generalizations of order statistic (OS) filters, a class of finite-width discrete windowing filters defined by linearly weighting the samples in the window according to their natural ordering as real numbers. The concept can be extended by defining generalized ordering rules generating different permutations of the sample prior to weighting. Although the resulting class of generalized OS filter is very broad (including, e.g. the linear filters), local signal ordering properties relating to local signal monotonicity unify them. It is envisaged that both the framework for filter/signal description and the class of filters generated will find use in many signal shaping applications