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arXiv · 1009.2043

Sampling and Recovery of Multidimensional Bandlimited Functions via Frames

Benjamin Aaron Bailey
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Abstract

In this paper, we investigate frames for $L_2[-π,π]^d$ consisting of exponential functions in connection to oversampling and nonuniform sampling of bandlimited functions. We derive a multidimensional nonuniform oversampling formula for bandlimited functions with a fairly general frequency domain. The stability of said formula under various perturbations in the sampled data is investigated, and a computationally managable simplification of the main oversampling theorem is given. Also, a generalization of Kadec's $1/4$ Theorem to higher dimensions is considered. Finally, the developed techniques are used to approximate biorthogonal functions of particular exponential Riesz bases for $L_2[-π,π]$, and a well known theorem of Levinson is recovered as a corollary.

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Benjamin Aaron Bailey. 2010-09-10. Sampling and Recovery of Multidimensional Bandlimited Functions via Frames. https://arxiv.org/abs/1009.2043

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