Exponential approximation of multivariate bandlimited functions from average oversampling

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 inverse Fourier transform decays at an optimal rate to zero at infinity.

Keywords:

• Average sampling
• exponential decayness
• multivariate bandlimited functions
• the Shannon sampling theorem

2010 Mathematical Subject Classifications:

• 41A25
• 62D05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported in part by Natural Science Foundation of China [11571377,11971490].