Generalized average sampling and reconstruction for wavelet subspaces

被引：0
作者：
Yugesh S. [1 ]
Devaraj P. [2 ]
机构：
[1] Department of Mathematics, SSN College of Engineering, Kalavakkam, 603110, Tamil Nadu
[2] School of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram, Maruthamala Post, Vithira, Thiruvananthapuram, 695551, Kerala
来源：
The Journal of Analysis | 2018年 / 26卷 / 2期
关键词：
Average sampling; Generalized average sampling; Wavelet space;
D O I：
10.1007/s41478-018-0148-8
中图分类号：
学科分类号：
摘要：
As an extension of the average sampling, we analyse generalized average sampling and reconstruction problem over some wavelet subspaces of L2(R). For closed subspaces V of L2(R) , we present a necessary and sufficient condition under which there is the generalized average sampling expansion for every f∈ V. © 2018, Forum D'Analystes, Chennai.
引用
收藏
页码：333 / 342
页数：9
相关论文
共 13 条
  • [1] Aldroubi A., Grochenig K., Nonuniform sampling and reconstruction in shift-invariant spaces, SIAM Review, 43, 4, pp. 585-620, (2001)
  • [2] Aldroubi A., Grochenig K., Beurling–Landau type theorems for non-uniform sampling in shift invariant spline spaces, The Journal of Fourier Analysis and Applications, 6, 1, pp. 93-103, (2000)
  • [3] Chen W., Itoh S., Shiki J., Irregular sampling theorems for wavelet subspaces, IEEE Transactions on Information Theory, 44, 3, pp. 1131-1142, (1998)
  • [4] Chui C.K., An Introduction to Wavelets, (1992)
  • [5] Janseen A.J.E.M., The Zak transform and sampling theorems for wavelet subspaces, IEEE Transactions on Signal Processing, 41, 12, pp. 3360-3364, (1993)
  • [6] Liu Y.M., Walter G.G., Irregular sampling in wavelet subspaces, The Journal of Fourier Analysis and Applications, 2, 2, pp. 181-189, (1995)
  • [7] Sun W., Zhou X., Frames and sampling theorem, Science in China (Series A), 41, 6, pp. 606-612, (1998)
  • [8] Sun W., Zhou X., Sampling theorem for wavelet subspaces: error estimate and irregular sampling, IEEE Transactions on Signal Processing, 48, 1, pp. 223-226, (2000)
  • [9] Sun W., Zhou X., Average sampling in spline subspaces, Applied Mathematics Letters, 15, pp. 233-237, (2002)
  • [10] Walter G.G., A sampling theorem for wavelet subspaces, IEEE Transactions on Information Theory, 38, 2, pp. 881-884, (1992)
12