MINIMUM-DURATION FILTERING

Myriad filtering and meridian filtering are known as robust methods of signal processing. The theory of these methods is based on the generalized Cauchy distribution and maximum-likelihood criterion. Based on the “Principle of Minimum Duration”, we present an alternative approach to justify and generalize the myriad and meridian filtering methods. The proposed approach shows that the myriad and meridian filtering methods are special cases of the minimum-duration filtering methods derived from a concept of “signal quasi-duration”. Mathematically, this concept is implemented through the concept of a functional (i.e., a function of a function) by using the proposed set of cost functions. On this foundation, a “superfamily” of quasi-duration functional is built, and a general class of minimum-duration filtering methods which depends on the three free-adjustable parameters is introduced. The numerical simulations are performed to compare the proposed and conventional methods for the problem of filtering a constant signal which is distorted by a mixture of Cauchy, Laplacian and Gaussian noise.