Affine order statistic filters: a data-adaptive filtering framework for nonstationary signals

We introduce a novel, data-adaptive, and robust ltering framework: a ne order-statistic lters. A ne order-statistics relate classical order-statistics to observations in their natural order and thus inherently yield a meaningful data representation. A ne order-statistic lters exploit this notion to adaptively process nonstationary signals. A ne order-statistic lters overcome many of the limitations associated with traditional order-statistic lters, in particular: lters in this class are parsimonious in the number of lter coe cients, they are statistically e cient in a wide range of signal statistics, and they admit real-valued lter weights leading to a wide-range of ltering characteristics. The class of a ne order statistic lters contains two families: the WOS a ne lter class whose structure can adapt, according to the observed data, from an FIR linear lter to a WOS lter, and the FIR a ne lter class whose structure can adapt from an Llter to an FIRlter. In this paper we introduce the median a ne lter and the center a ne lter as representatives of each class, and show their performance in two applications where the signals are non-stationary in nature.