Theory of order statistic filters and their relationship to linear FIR filters

Necessary and/or sufficient conditions on both the filter coefficients and the signal process are derived in order that nonrecursive order statistic (OS) and linear filtering are equivalent operations. The results indicate that an understanding of OS filters hinges on a better understanding of the properties of signals containing logically monotonic components. The results extend a number of previous theories characterizing the well-known median and ranked-order filters to a broader class of filters and input signals