A new design methodology for L-filters

L-filters are very successful at restoration of signals corrupted by noise. However, their on-line design in real-time applications is practically impossible, since the computation of optimal L-filter coefficients with the existing methods based on numerical approximations are extremely time consuming. In this paper, we present a new design methodology for L-filters. Our approach allows one to compute the desired filter coefficients by just evaluating the inverse cumulative distribution function and the probability density function of the underlying noise at n different points, where n is the sample size. The presented design method is derived by approximating the inverse covariance matrix of ordered random variables and simplifying the closed-form solution of optimal L-filter coefficients. The comparisons with the classical approach and the simulations show that the proposed method is very promising for a wide range of noise types.