Selection filters and commutativity with memoryless nonlinearities

A class of nonrecursive filters that commute with every increasing zero-memory nonlinear (ZNL) transformation is characterized. Specifically, it is shown that a nonrecursive filter commutes with every increasing ZNL transformation if and only if it is a rank-based selection (RBS) filter that replaces each input value with one of its neighboring input datum (which is selected depending on relative amplitudes of the data). It is also shown that RBS filters commuting with every nondecreasing ZNL transformation are stack filters that can be represented as finite maximum-minimum operations