Impulsive noise cancelation with simplified Cauchy-based p-norm filter

This paper addresses the problem of impulsive noise cancelation in digital signal processing area. The myriad and meridian filters are the type of robust filters which are very useful in suppressing the impulsive type of noise. These filters belong to the family of the robust M-filters and are controlled with only one parameter. The common property of these filters is the way of operating. They are a running window filters outputting the sample myriad or meridian of elements in the window. The cost functions of these filters have very similar structure. Its form is always log function which contains a constant and some expression that can be replaced with the p-th power of the general ^Lp-norm formula. In this paper the simplified Cauchy-based p-norm filter is presented. The proposed filter operates in a wide range of impulsive noise due to the proper adjustment of p exponent of the ^Lp-norm. The presented filter is applied to suppress an impulsive noise in testing chirp signal and in power line communications environment. Simulations results confirm the validity of the derived method of filtering and good performance of the proposed simplified Cauchy p-norm filter.