Robust frequency-selective filtering using Weighted Sum-Median filters

Mean-Median (MEM) filters, based on two-component mixture distributions, are recently proposed [1]. The MEM filter output is a combination of the sample mean and the sample median, where observation samples are weighted uniformly. This property of MEM filters constrains them to the class of smoothers. This paper extends MEM filtering to the Weighted Sum-Median (WSM) filtering structure admitting real-valued weights, thereby enabling more general filtering characteristics. The proposed filter structure is also well-motivated from a presented maximum likeihood (ML) estimate analysis under E-contaminated statistics. The combination parameter a is optimized to minimize the filter output variance, which is a measure of noise attenuation capability. Moreover, filter design procedures that yield a desired spectral response are detailed. Finally, the effectiveness of the proposed WSM filter structure is shown through simulations.