The analog median filter

Discrete median filters are a special class of ranked-order digital filters used for smoothing signals. In this paper, the analog median filter is defined and proposed for analysis of the standard discrete median filter in cases with a large sample size or when the associated statistics would be simpler in the continuum. Discrete filters are shown to be a subclass of analog filters. Also, an equivalence among analog filters and limits of discrete filters is established. Finally, several stochastic interpretations of the analog median filter are presented including necessary and sufficient conditions on input processes which guarantee the existence of output distributions for multiple passes of the analog median filter