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Recovery of Missing Samples in Oversampling Formulas Band Limited  Functions

Abstract:
In a previous paper we 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.

Keywords:
Frame, Risz-basis,shift-invariant space,sampling formulas,band-limited functions

MSC:
42, 46

Pubblicato su: Sampling Theory in Signal and Image Processing. An International Journal Vol. 8 (2009) N. 2 Pag. 161-180