Exponential Approximation of Multivariate Bandlimited Functions from Average Oversampling

Wenjian Chen; Haizhang Zhang

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arXiv · 1412.4265

Exponential Approximation of Multivariate Bandlimited Functions from Average Oversampling

Wenjian Chen·Haizhang Zhang

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Abstract

Instead of sampling a function at a single point, average sampling takes the weighted sum of function values around the point. Such a sampling strategy is more practical and more stable. In this note, we present an explicit method with an exponentially-decaying approximation error to reconstruct a multivariate bandlimited function from its finite average oversampling data. The key problem in our analysis is how to extend a function so that its Fourier transform decays at an optimal rate to zero at infinity.

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Wenjian Chen, Haizhang Zhang. 2014-12-13. Exponential Approximation of Multivariate Bandlimited Functions from Average Oversampling. https://arxiv.org/abs/1412.4265

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