多元Whittaker-Shannon采样展开的截断误差
Truncation Errors for Multi-Dimensional Whittaker-Shannon Sampling Expansion
DOI: 10.12677/AAM.2018.75064, PDF,  被引量    国家自然科学基金支持
作者: 王桐心：王桐心，陈 锦，陆文静，韩永杰；陈 锦, 陆文静, 韩永杰：西华大学理学院，四川 成都
关键词: 有限带宽函数；Whittaker-Shannon定理；局部采样；截断误差；Band-Limited Functions； Whittaker-Shannon Theorem； Localized Sampling； Truncation Error
摘要: 本文利用线性泛函构造采样级数，研究了一个覆盖几个误差的通用模型。并考虑了在无衰减假设条件下，Paley-Wiener函数类B2V(ℝd)的截断误差的最优边界。
Abstract: In this paper, we study a general model that uses linear functionals to cover several errors in one formula, consider sampling series with measured sampled values for band limited signals without decay assumption, and obtain the optimal bounds of truncation errors for band limited signal functions from Paley-Wiener spaceB2V(ℝd).
文章引用：王桐心, 陈锦, 陆文静, 韩永杰. 多元Whittaker-Shannon采样展开的截断误差[J]. 应用数学进展, 2018, 7(5): 525-529. https://doi.org/10.12677/AAM.2018.75064

参考文献

[1] Nikolskii, S.M. (1975) Approximation of Functions of Several Variables and Imbedding Theorems. Springer-Verlag, Ber-lin/Heidelberg, New York.
[2] Shannon, C.E. (1948) A Mathematical Theory of Communication. Bell System Technical Journal, 27, 397-423, 623-656.
[3] Wang, J.J. and Fang, G.S. (1996) Multidimensional Sampling Theorem and Estimate of Aliasing Error. ACTA Mathematicae Applicatae Sinica, 19, 481-488. (In Chinese)
[4] Li, X.M. (1998) Uniform Bounds for Sampling Expansions. Journal of Approximation Theory, 93, 100-113.
[Google Scholar] [CrossRef] 
[5] Long, J.F. and Fang, G.S. (2003) On Uniform Truncation Error Bounds and Aliasing Error for Multidimensional Sampling Expansion. Sampling Theory in Signal and Image Processing, 2, 103-115.
[6] Helms, H.D. and Thomas, J.B. (1962) Truncation Error of Sampling-Theorem Expansions. Proceedings of the IRE, 50, 179-184.
[Google Scholar] [CrossRef] 
[7] Jagerman, D. (1966) Bounds for Truncation Error of the Sampling Expansion. SIAM Journal on Applied Mathematics, 14, 714-723.
[Google Scholar] [CrossRef] 
[8] Micchelli, C.A., Xu, Y.S. and Zhang, H.Z. (2009) Optimal Learning of Bandlimited Functions from Localized Sampling. Journal of Complexity, 25, 85-114.
[Google Scholar] [CrossRef] 
[9] Boas Jr., R.P. (1954) Entire Functions. Academic Press, New York.

为你推荐