Root properties and convergence rates of median filters

Median filters are a special class of ranked order filters used for smoothing signals. Repeated application of the filter on a quantized signal of finite length ultimately results in a sequence, termed a root signal, which is invariant to additional passes of the median filter. In this paper, the theory is developed both for determining the cardinality of the root signal space of arbitrary window width filters applied to signals with any number of quantization levels and for counting or estimating the number of passes required to produce a root for binary signals.