Some properties of a class of rank order smoothers

A class of rank order smoothers, which operate by minimizing a piecewise linear objective function, is considered. Nonrecursive versions have many properties similar to repeated median smoothing, and most of these properties are relevant, with qualifications, to recursive versions of the class. Smoothed values are medians in their neighborhoods. A root signal is obtained, but advantageously in only one application of the algorithm. Pulses can be passed or rejected, and monotone sequences passed, in ways similar to median smoothers. Bit serial algorithms are applicable to both, in similar senses.