Open Access
April, 1995 Reconstruction of Band Limited Processes from Irregular Samples
Christian Houdre
Ann. Probab. 23(2): 674-696 (April, 1995). DOI: 10.1214/aop/1176988284


The problem of recovering, say, a band-limited weakly stationary process from a set of its irregularly spaced samples is studied. For rather general sampling sequences some sufficient conditions ensuring mean square or pathwise reconstruction are obtained. For the cases of regular samples with either finitely many missing ones and/or finitely many irregular ones, a necessary and sufficient condition is presented. Some elements of the proofs involve classical results on nonharmonic Fourier series as well as more recent results on frames.


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Christian Houdre. "Reconstruction of Band Limited Processes from Irregular Samples." Ann. Probab. 23 (2) 674 - 696, April, 1995.


Published: April, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0836.60050
MathSciNet: MR1334166
Digital Object Identifier: 10.1214/aop/1176988284

Primary: 60F15
Secondary: 60F25 , 60G12 , 60G25

Keywords: $L^\alpha$ and almost everywhere convergence , band-limited processes , frames , Irregular sampling , missing data , nonstationary processes

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 2 • April, 1995
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