Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

FRAME AND LATTICE SAMPLING THEOREM FOR SUBSPACES OF $L^2$��

  • Liu, Zhan-Wei (Department of Applied Mathematics, University of Information Engineering) ;
  • Hu, Guo-En (Department of Applied Mathematics, University of Information Engineering)
  • Published : 2009.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, a necessary and sufficient condition for lattice sampling theorem to hold for frame in subspaces of $L^2$(R) is established. In addition, we obtain the formula of lattice sampling function in frequency space. Furthermore, by discussing the parameters in Theorem 3.1, some corresponding corollaries are derived.

Keywords

References

  1. G. G. Walter, A sampling theorem for wavelet subspaces, IEEE Trans. Inform. Theory 38(1992), 881-884. https://doi.org/10.1109/18.119745
  2. X. G. Xia and Z. Zhang, On sampling theorem, wavelet and wavelet transforms, IEEE Trans. Signal Processing 41(1993), 3524-3535. https://doi.org/10.1109/78.258090
  3. A. J. E. M. Janssen, The Zak transform and sampling theorems for wavelet subspaces, IEEE Trans. Signal Processing 41(1993), 3360-3365. https://doi.org/10.1109/78.258079
  4. Y. Liu, Irregular sampling for spline wavelet subspaces, IEEE Trans. Inform. Theory 42(1996), 623-627. https://doi.org/10.1109/18.485731
  5. W. Chen, S. Itoh and J. Shiki, A sampling theorem for shift-invariant spaces, IEEE Trans. Signal Processing 46(1998), 2802-2810.
  6. P. Zhao, G. Z. Liu and C. Zhao, Frames and Sampling Theorems for Translation-Invariant Subspaces, IEEE Trans. Signal Processing 11(2004), 8-11. https://doi.org/10.1109/LSP.2003.819357
  7. J. J. Benedetto and S. Li, Multiresolution analysis frames with subspace, in Proc ICASSP 3 Minneapolis MN Apr 26-30(1993), 304-307.