Science in China Series A: Mathematics

, Volume 41, Issue 6, pp 606–612 | Cite as

Frames and sampling theorem

  • Wenchang Sun
  • Xingwei Zhou
Article

Abstract

The sampling problem on a closed subspace Vo of L2(ℝ) is studied. For the regular sampling, a necessary and sufficient condition on the sampling theorem is presented and the sampling problem proposed by Walter is completely solved. Moreover, a representation formula for the derived function is given. The irregular sampling is studied. The results improve the ones of Walter and Liu’s.

Keywords

frames sampling wavelets 

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References

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    Walter, G. G., A sampling theorem for wavelet subspaces,IEEE Trans. Inform. Theory, 1992, 38(2): 881.CrossRefMathSciNetGoogle Scholar
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    Liu, Y., Walter, G., Irregular sampling in wavelet subspaces,The Journal of Fourier Analysis and Applications, 1995, 2(2): 181.MATHCrossRefMathSciNetGoogle Scholar
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    Daubechies, I.,Ten Lectures on Wavelets, Philadelphia: SIAM, 1992.MATHGoogle Scholar
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    Chui, C. K.,An introduction to Wavelets, San Diego: Academic Press, 1992.MATHGoogle Scholar

Copyright information

© Science in China Press 1998

Authors and Affiliations

  • Wenchang Sun
    • 1
  • Xingwei Zhou
    • 1
  1. 1.Department of MathematicsNankai UniversityTianjinChina

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