Frontiers of Mathematics in China >

2006 , Vol. 1 >Issue 2: 252 - 271

DOI: https://doi.org/10.1007/s11464-006-0006-x

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

Expand
  • 1.College of Sciences, North China University of Technology, Beijing 100041, China; 2.School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;

Published date: 05 Jun 2006

Fold

Abstract

Denote by B2σ,p (1 < p < ") the bandlimited class p-integrable functions whose Fourier transform is supported in the interval [-?, ?]. It is shown that a function in B2σ,p can be reconstructed in Lp(R) by its sampling sequences {f(k?/?)}k∈Z and{f 2(k?/?)}k∈Z using the Hermite cardinal interpolation. Moreover, it will be shown that if f belongs to Lpr(R), 1 < p < ∞, then the exact order of its aliasing error can be determined.

Cite this article

LI Hu-an, FANG Gen-sun . Sampling theorem of Hermite type and aliasing error on the Sobolev class of functions[J]. Frontiers of Mathematics in China, 2006 , 1(2) : 252 -271 . DOI: 10.1007/s11464-006-0006-x

Options
Outlines

/

〈 〉