Weighted median based filters for the complex domain

Weighted median (WM) filtering structures for complex-valued samples have been proposed but none of them allows the use of complex-valued weights. This paper defines complex-valued weighting for median filters with complex-valued input samples. Two different approaches to the handling of weights in the complex domain are presented, both derived from characteristics of complex-valued linear filters, resulting in two definitions of the complex weighted median filter. The LMS optimizations of the proposed filtering schemes are also presented. Simulations are shown illustrating the performance of the new complex WM filter structures compared with previous approaches to the problem and with classical linear filters.