Zak Transform and Sampling Theorem in the Shift Invariant Subspace

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- Zak Transform and Sampling Theorem in the Shift Invariant Subspace
- Vol. 41, Issue 10, Pages: 1248-1250(2007)
- 作者机构：
  
  西安交通大学理学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： O174.2
- Online First：10 October 2007，
  
  Published：2007
- 稿件说明：
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吴国昌 1, 程正兴 1, 赵江涛 2. Zak Transform and Sampling Theorem in the Shift Invariant Subspace[J]. 2007, 41(10): 1248-1250.
DOI：

吴国昌 1, 程正兴 1, 赵江涛 2. Zak Transform and Sampling Theorem in the Shift Invariant Subspace[J]. 2007, 41(10): 1248-1250. DOI：

研究了平移不变子空间中的抽样定理

首先通过Zak变换刻画了抽样空间的一些性质

然后证明了在一个平移不变的抽样空间中

由其中任一个函数的整平移所张成的子空间也是抽样空间

即在平移不变子空间中

抽样性质具有遗传性.最后给出了函数满足抽样定理的一些必要条件.

Shannon C E. Communication in the presence of noise[J].Proc IRE, 1949,37(1):10-21.

Zhou X, Sun W.On the sampling theorem for wavelet subspaces[J]. J Fourier Anal Appl,1999,5(4):347-354.

Sun W, Zhou X. An aspect of the sampling theorem[J].International Journal of Wavelets, Multire solution and Information Processing,2005,3(2):247-255.

Sun W. Sampling theorems for multivariate shift invariant subspaces[J].Sampl Theory Signal Image Process,2005,4(1):73-98.

Blance C, Cabrelli C,Heineken S.Functions in sampling spaces[J].Sampl Theory Signal Image Process, 2005,5(3):275-295.

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