Root Signals of Rank Order Processors

A rank order processor (ROP) is a signal processor that operates purely by making rank determinations on input values, and includes as special cases “median filters” and “rank order filters.” It is shown how the methods of automata theory can be used to show the existence of root signal (i.e., fixed point) sets of input sequences, and to determine them for specific ROP’s, in either algebraic or graphical form. Observations on graph/subgraph relationships are made. It is shown how certain earlier methods of determining root signals can be improved and extended to the general case. Remarks on the synthesis problem are made.