2014/12/13 by Wenjian Chen, Chen, Wenjian, Haizhang Zhang +1
Computer Science · Mathematics · #41A25 #62D05 #Digital Filter Design and Implementation #FOS: Computer and information sciences #Image and Signal Denoising Methods #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1412.4265
openalex publication_date 2014/12/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.