Recovery of Missing Samples in Oversampling Formulas for Band Limited Functions

Details Recovery of Missing Samples in Oversampling Formulas for Band Limited Functions Recovery of Missing Samples in Oversampling Formulas for Band Limited Functions

2008-11-02

arxiv.org/abs/0811.0149v2

Mathematics

Functional Analysis

19 pages, 3 figures, corrected a few typos

Scientific paper

In a previous paper, the author constructed frames and oversampling formulas for band-limited functions, in the framework of the theory of shift-invariant spaces. In this article we study the problem of recovering missing samples. We find a sufficient condition for the recovery of a finite set of missing samples. The condition is expressed as a linear independence of the components of a vector W over the space of trigonometric polynomials determined by the frequencies of the missing samples. We apply the theory to the derivative sampling of any order and we illustrate our results with a numerical experiment.

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