Uniform Bounds of Aliasing and Truncated Errors in Sampling Series of Functions from Anisotropic Besov Class
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-06-23
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
Errors appear when the Shannon sampling series is applied to approximate a signal in real life.
This is because a signal may not be bandlimited, the sampling series may have to be truncated, and the sampled values may not be exact and may have to be quantized.
In this paper, we truncate the multidimensional Shannon sampling series via localized sampling and obtain the uniform bounds of aliasing and truncation errors for functions from anisotropic Besov class without any decay assumption.
The bounds are optimal up to a logarithmic factor.
Moreover, we derive the corresponding results for the case that the sampled values are given by a linear functional and its integer translations.
Finally we give some applications.
American Psychological Association (APA)
Ye, Peixin& Han, Yongjie. 2013. Uniform Bounds of Aliasing and Truncated Errors in Sampling Series of Functions from Anisotropic Besov Class. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-450174
Modern Language Association (MLA)
Ye, Peixin& Han, Yongjie. Uniform Bounds of Aliasing and Truncated Errors in Sampling Series of Functions from Anisotropic Besov Class. Abstract and Applied Analysis No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-450174
American Medical Association (AMA)
Ye, Peixin& Han, Yongjie. Uniform Bounds of Aliasing and Truncated Errors in Sampling Series of Functions from Anisotropic Besov Class. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-450174
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-450174