REGULAR SETS AND RANK ORDER PROCESSORS

Rank order processors (ROP’s) may 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 illustrate advantages of such specification partly 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 ROP’s, although not implementable as finite autoregressive algorithms involving only the input-output signal values, are implementable as finite state sequential machines, e.g., employing a modified “stack filter” structure. The demonstration is constructive and coincidentally shows how the idea of a “nondeterministic” automaton relates to the subject matter. © 1990 IEEE