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    Abstract:

    Sampling theory is one of the most powerful results in modern information theory and technology. The digital signal with sampling properties can be reconstructed from its samples in a perfect form. Walter and Zhou extended the Shannon sampling theorem to wavelet subspaces. This paper improves the classical sampling theorems based on wavelet frames. A basic problem on information theory is introduced here. For a given digital signal, whether it has sampling series form. In this paper, the digital signals with sampling properties are characterized based on wavelet frames. For a given sapling subspace, the analytic form of the signals in it is proposed. Especially some new kinds of sampling subspaces are offered here. As an application, the examples show that the new theorems improve some known relating results, which is effective for the digital signals’ sampling and reconstructions.

    Reference
    [1] Walter G. A sampling theorem for wavelet subspaces. IEEE Trans. on Inform. Theory, 1992,38(2):881?884.
    [2] Zhou XW, Sun WC. On the sampling theorem for wavelet subspace. J. Fourier Anal. Appl., 1999,5(4):347?354.
    [3] Boor C, Devore R, Ron A. The structure of finitely generated shift-invariant subspaces in L2(Rn). J. Func. Anal., 1994,119(1):37?78.
    [4] Boor C, Devore R, Ron A. Approximation from shift-invariant subspaces of L2(R). Trans. Amer. Math, Soc., 1994,341:787?806.
    [5] Bownik M. The structure of shift-invariant subspace of L2(Rn). J. Func. Anal., 2000,177(2):282?309.
    [6] Ron A, Shen ZW. Frames and stable bases for shift-invariant subspaces of L2(Rd). Can. J. Math., 1995,5:1051?1094.
    [7] Christensen O. An Introduction to Frames and Riesz Bases. Boston: Birkhauser, 2003.
    [8] Zhao C, Zhao P. Sampling theorem and irregular sampling theorem for multiwavelet subspaces. IEEE Trans. on Signal Processing, 2005,53(2):705?713.
    [9] Li XZ, Yang DY. A further characterization on the sampling theorem for wavelet subspaces. In: Computational Science-ICCS. LNCS 4488, 2007. 1021?1028.
    [10] Yang DY, Zhou XW, Yuan ZZ. Frame wavelets with compact supports for L2(Rn). Acta Mathematica Sinica, English Series, 2007, 23(2):349?356.
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杨德运,李秀珍,桑胜举,侯迎坤,刘明霞.一类基于小波框架的采样子空间.软件学报,2009,20(zk):231-238

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History
  • Received:March 05,2009
  • Revised:April 03,2009
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