Abstract
Suppose thatx=|x(n)|n∈ℤ is a sequence of real numbers. For eachp∈ℕ,x p=|x p(n)|n∈ℤis the resulting sequence ofx throughp times median filterings with window 2k+1. It is proved that whenp→∞, bothx (2p) andx(2 p}-1) are convergent. Thus the problem of convergence of the median filters of infinite-length sequences is completely solved.
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Project supported by the National Natural Science Foundation of China (Grant No. 16971047).
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Ye, W., Zhou, X. Convergence of the median filterings of sequences. Sci. China Ser. A-Math. 42, 382–386 (1999). https://doi.org/10.1007/BF02874256
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DOI: https://doi.org/10.1007/BF02874256