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Average sampling and reconstruction for reproducing kernel stochastic signals
Author(s) -
Jiang Yingchun,
Wang Suping,
Yang Meixiang
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3740
Subject(s) - mathematics , kernel (algebra) , autocorrelation , convergence (economics) , bounded function , sampling (signal processing) , quadratic equation , frame (networking) , mathematical optimization , algorithm , mathematical analysis , combinatorics , statistics , computer science , geometry , telecommunications , filter (signal processing) , economics , computer vision , economic growth
This paper mainly considers the problem of reconstructing a reproducing kernel stochastic signal from its average samples. First, a uniform convergence result for reconstructing the deterministic reproducing kernel signals by an iterative algorithm is established. Then, we prove that the quadratic sum of the corresponding reconstructed functions is uniformly bounded. Moreover, the reconstructed functions provide a frame expansion in the special case p = 2. Finally, the mean square convergence for recovering a weighted reproducing kernel stochastic signal from its average samples is given under some decay condition for the autocorrelation function, which can be removed for the case p = 2. Copyright © 2015 John Wiley & Sons, Ltd.