The variation of a discrete signal is defined and used as a measure of roughness. It is shown that the median filter does not increase the variation of a signal, supporting the perception of the median filter as a smoother. Signals of both finite and infinite lengths are considered; for signals of finite length, nonpadding median filters are used.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
