Research Article | OPEN ACCESS
Error Analysis for Shannon Sampling Series Approximation with Measured Sampled Values
Peixin Ye
School of Mathematics and LPMC, Nankai University, Tianjin, 300071, P.R. China
Research Journal of Applied Sciences, Engineering and Technology 2013 3:858-864
Received: June 13, 2012 | Accepted: July 18, 2012 | Published: January 21, 2013
Abstract
Errors appear when the Shannon sampling series is applied to reconstruct a signal in practice. In this paper, we study a general model that uses linear functional to cover several errors in one formula, and consider sampling series with measured sampled values for not band-limited signals but satisfying some decay condition. We obtain the uniform truncated error bound of Shannon series approximation for multivariate Besov class. The results show this kind of Shannon series can approximate a smooth signal well.
Keywords:
Besov class, local averages, measured sampled values, modulus of continuity, Shannon sampling theorem, truncation error,
Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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