Sampling theorem of Hermite type and aliasing error on the Sobolev class of functions

DOI10.1007/s11464-006-0006-xzbMath1222.42004OpenAlexW1518643608MaRDI QIDQ719970

Hu-An Li, Gen Sun Fang

Publication date: 12 October 2011

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11464-006-0006-x

zbMATH Keywords

aliasing errorbandlimited functionderivative samplingMarcinkiewicz type inequalitySobolev classes of functions

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Trigonometric approximation (42A10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10)

Related Items (4)

Hermite interpolation theorems for band-limited functions of the linear canonical transforms with equidistant samples ⋮ A bivariate sampling series involving mixed partial derivatives ⋮ On divergence of sinc-approximations everywhere on $(0,\pi)$ ⋮ A Modification of Hermite Sampling with a Gaussian Multiplier

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Mathematical Theory of Communication
• The Euler-MacLaurin summation formula, the sampling theorem, and approximate integration over the real axis
• On the \(L^ p\) convergence of Lagrange interpolating entire functions of exponential type
• Irregular sampling of bandlimited \(L^ p\)-functions
• Whittaker-Kotelnikov-Shannon sampling theorem and aliasing error
• Approximating properties of entire functions of exponential type
• On the error in reconstructing a non-bandlimited function by means of the bandpass sampling theorem
• Five short stories about the cardinal series
• Sampling Theory for not Necessarily Band-Limited Functions: A Historical Overview
• A sampling theorem for duration-limited functions with error estimates
• An Extension of Carlson's Theorem for Entire Functions of Exponential Type
• On Lacunary Trigonometric Series
• On the General Hermite Cardinal Interpolation

This page was built for publication: Sampling theorem of Hermite type and aliasing error on the Sobolev class of functions