Regular sets and rank order processors

Rank order processors (ROPs) can be specified in terms of regular sets and consequently studied as finite-state automata or sequential machines. A necessary and sufficient condition for a regular set to represent an ROP is given. Examples are given to illustrate the advantages of such a specification in terms of a primary focus on root signals and input-output relations. One result is a practical equivalent of the recursive median smoother that is easier to compute. Another is a demonstration that some ROPs, although not implementable as finite autoregressive algorithms involving only the input-output signal values, are implementable as finite state sequential machines, e.g. those with a modified stack filter structure. The demonstration is constructive and coincidentally shows how the idea of a nondeterministic automaton relates to the subject matter