Smoothed median filters with FIR substructures

In this paper we introduce a new generalized class of Median Filters (MF) which we call Smoothed Median Filters (SMF). The input signal x(n) is filtered with M linear phase FIR filters and the output of the SMF is the median of the outputs of the FIR filters. The statistical properties of the SMF´s are analyzed for input signals with Gaussian, double exponential, and uniform density functions. It is shown that SMF´s have essentially the same statistical properties and same type of root signals as the conventional MF´s. SMF´s preserve corner points and ramps and attenuate impulsive type noise components effectively. An interesting subclass of the SMF´s requiring only two scaling multipliers and three data sorting operations irrespective of the filter length is introduced.