AN ADAPTIVE RECURSIVE WEIGHTED FILTER BASED ON THE MYRIAD OPERATOR

Abstract

In this paper, we introduce a new family of nonlinear filters based on the Myriad operator. The proposed approach introduces recursivity into the filtering operation where previous filter outputs are fedbacked into the filtering operation to conform an observation window that has input samples and previous filtered values leading thus to a recursive Weighted Myriad filter (RWMy). The proposed filtering structure is equipped with a tunning parameter that allow to set the degree on impulsiveness rejection capability. Thus, as that parameter goes to infinity the RWMy reduces to the well-known Infinity Impulse response (IIR) filter which has been proven to outperform the finite impulse response (FIR) filter. Furthermore, an adaptive optimization algorithm based on equation error formulation is also proposed for the design of RWMy where an absolute error cost function is minimized at each iteration. Extensive computer simulations show that the proposed approach outperforms the no recursive version much like the IIR outperforms the FIR filters.