Median Filtering of Deterministic and Stationary Stochastic Signals

The notion of media filtering (MF) of a continuous time process was introduced in [L. I. Piterbarg, Probl. Peredachi Inf., 1984, vol. 20, no. 1, pp. 65–73], where we determined the rate of convergence of the statistical characteristics of the output signal to the corresponding characteristics of the input signal with the window width going to zero for some normal processes. In this paper, the previous results are generalized to arbitrary stationary processes. We investigate the robustness of the media with respect to a thinning stream of impulse noise. The analysis of the stochastic case is preceded by a number of propositions relating to MF of deterministic signals.