Convergence of symmetric weighted median filters

Abstract

Suppose that χ = {χ(n)}_n∈z is a sequence of real numbers. For each p ∈ N, χ^(p) = {χ^(p)(n)}_n∈z is the resulting sequence of χ through p times symmtric weighted median filters with window 2k + 1. It is proved that when p → ∞, both χ^(2p) and χ^(2p-1) are convergent.