Proceedings PaperSome properties of order statistic filters
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Let X1, X2, ... be a stationary sequence of random variables with Pr(Xt less than or equal to x) = F(x), t = 1, 2, ... . Also let Xi:n(t), i = 1, ..., n, denote the i-th order statistic (OS) in the moving sample (Xt-N, ..., Xt, ..., Xt+N) of odd size n = 2N + 1. Then Yt = (summation)aiXi:n(t) with (summation)ai = 1 is an order statistics filter. In practice ai greater than or equal to 0, i = 1, ..., n. For t > N, the sequence (Yt) is also stationary. If X1, X2, ... are independent, the autocorrelation function ρ(r) = corr(Yt, Tt+r) is zero for r > n-1 and for r less than or equal to n-l can be evaluated directly in terms of the means, variances, and covariances of the OS in random samples of size n + r from F(x). In special cases several authors have observed that (Yt) produces a low-pass filter. It will be shown that this result holds generally under white noise. The effect of outliers (impulses) is also discussed.