Science in China Series A: Mathematics

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

Frames and sampling theorem

  • Wenchang Sun
  • Xingwei Zhou


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.


frames sampling wavelets 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Walter, G. G., A sampling theorem for wavelet subspaces,IEEE Trans. Inform. Theory, 1992, 38(2): 881.CrossRefMathSciNetGoogle Scholar
  2. 2.
    Liu, Y., Walter, G., Irregular sampling in wavelet subspaces,The Journal of Fourier Analysis and Applications, 1995, 2(2): 181.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Long, R. L.,Multidimensional Wavelet Analysis (in Chinese), Beijing: Word Publishing Corporation, 1995, 3–27.Google Scholar
  4. 4.
    Daubechies, I.,Ten Lectures on Wavelets, Philadelphia: SIAM, 1992.MATHGoogle Scholar
  5. 5.
    Benedetto, J. J., Heil, C., Walnut, D. F., Differentiation and the Balian-Low theorem,J. Four. Anal. Appl., 1995, 1(4): 355.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    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

Personalised recommendations