Convergence Analysis of the Gaussian Regularized Shannon Sampling Series

DOI10.1080/01630563.2016.1240182zbMath1386.94054arXiv1601.01363OpenAlexW2400968058MaRDI QIDQ2987794

Haizhang Zhang, Rongrong Lin

Publication date: 18 May 2017

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.01363

zbMATH Keywords

oversamplingbandlimited functionsaverage samplingGaussian regularizationShannon's sampling series

Mathematics Subject Classification ID

Sampling theory, sample surveys (62D05) Rate of convergence, degree of approximation (41A25) Sampling theory in information and communication theory (94A20)

Related Items (6)

On multidimensional sinc-Gauss sampling formulas for analytic functions ⋮ A multidimensional Hermite-Gauss sampling formula for analytic functions of several variables ⋮ An Optimal Convergence Rate for the Gaussian Regularized Shannon Sampling Series ⋮ Gaussian regularized periodic nonuniform sampling series ⋮ Sharp exponential bounds for the Gaussian regularized Whittaker-Kotelnikov-Shannon sampling series ⋮ On regularized Shannon sampling formulas with localized sampling

Cites Work

• Unnamed Item
• Convolution, average sampling, and a Calderon resolution of the identity for shift-invariant spaces
• Optimal learning of bandlimited functions from localized sampling
• Reconstruction of band-limited functions from local averages
• Non-uniform weighted average sampling and reconstruction in shift-invariant and wavelet spaces
• Discrete singular convolution for the sine-Gordon equation
• On the validity of ``A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximation function (LDAF) method is inferior to high order finite differences by J. P. Boyd.
• The Shannon sampling theorem—Its various extensions and applications: A tutorial review
• Reconstruction Algorithms in Irregular Sampling
• Comparison of the Discrete Singular Convolution and Three Other Numerical Schemes for Solving Fisher's Equation
• Reconstruction of band-limited signals from local averages
• On the regularized Whittaker-Kotel’nikov-Shannon sampling formula
• Bounds for Truncation Error of the Sampling Expansion
• \(p\)-frames and shift invariant subspaces of \(L^p\)

This page was built for publication: Convergence Analysis of the Gaussian Regularized Shannon Sampling Series