ISSN:
1531-5878
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract LetX 1,X 2,... be a stationary sequence of random variables with Pr{X t, ≤x}=F(x),t=1, 2,... Also let i ∶n,(t) ,i=1,...,n, denote the ith order statistic (OS) in the moving sample (X t−N ,...,X t,...,X t+N) of odd sizen=2N+1. ThenY t=∑a i X i ∶n(t) with ∑a i=1 is an order-statistics filter. In practicea i≥0,i=1,...,n. Fort〉N, the sequence {Y t} is also stationary. IfX 1 X 2, ... are independent, the autocorrelation function ρ(r)=corr(Y t,Y t+r) is zero forr 〉n − 1 and forr ≤n − 1 can be evaluated directly in terms of the means, variances, and covariances of the OS in random samples of sizen +r fromF(x). In special cases several authors have observed that the spectral density functionf(ω) of {Y t} is initially decreasing for ω 〉 0. This result is made more precise and shown to hold generally under white noise. The effect of outliers (impulses) is also discussed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01189222
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