Sampled-function weighted order filters

Abstract

In this paper, a new type of L-filter, called a sampled-function weighted order (SFWO) filter is proposed. The coefficients of this filter are samples of a bounded real-valued function. This weighting function is derived for any given noise distribution by examining the asymptotic behavior of the corresponding L-filter coefficients. SFWO filters designed in this way constitute a good compromise between alpha-trimmed mean filters, which are easy to design, and optimal L-filters, which are more flexible but difficult to design. In fact, for a given class of distributions, a SFWO filter can be designed in the form of a smoothly-trimmed mean filter with one or more parameters and can perform as well as the optimal L-filter for that class. Design examples are given for Gaussian, Laplacian, Cauchy, triangular, parabolic, and uniform noise densities. Simulations show that SFWO filters are very promising for noise densities, the tail lengths of which vary from very short to very long.