Relating analog and digital order statistic filters

Recent efforts have been directed towards the development of analog versions of the digital median filter. Here, the concept is extended to the more general rank-order and order statistic (OS) filters. By identifying analog and digital signals that are in some sense equivalent, such that the outputs of analog and digital OS filters applied to equivalent analog and digital signals are also equivalent, the properties of discrete-time and continuous-time OS filters can be related, making possible a richer mathematical framework for analysis and design of rank-order and OS filters in both domains. While some theory for digital rank-order and OS filters has been developed, the definition of the analog versions is nontrivial. Suitable definitions are offered for analog versions of the rank-order and OS filters, and a formalism is developed for relating the analog and digital filters