Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2012, Article ID 746823, 14 pages
http://dx.doi.org/10.1155/2012/746823
Research Article

Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ

1Department of Mathematics, Shantou University, Guangdong, Shantou 515063, China
2Department of Mathematics, Hanshan Normal University, Guangdong, Chaozhou 521041, China

Received 10 March 2012; Accepted 19 May 2012

Academic Editor: Sergey V. Zelik

Copyright © 2012 D. H. Yuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Zibulski and Y. Y. Zeevi, “Discrete multiwindow Gabor-type transforms,” IEEE Transactions on Signal Processing, vol. 45, no. 6, pp. 1428–1442, 1997. View at Google Scholar
  2. M. Zibulski and Y. Y. Zeevi, “Analysis of multiwindow Gabor-type schemes by frame methods,” Applied and Computational Harmonic Analysis, vol. 4, no. 2, pp. 188–221, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. A. Akan and L. F. Chaparro, “Multi-window Gabor expansion for evolutionary spectral analysis,” IEEE Transactions on Signal Processing, vol. 63, no. 3, pp. 249–262, 1997. View at Google Scholar
  4. S. Li, “Discrete multi-Gabor expansions,” IEEE Transactions on Information Theory, vol. 45, no. 6, pp. 1954–1967, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. S. Li, “Proportional nonuniform multi-Gabor expansions,” EURASIP Journal on Applied Signal Processing, vol. 17, pp. 2723–2731, 2004. View at Google Scholar
  6. N. K. Subbanna and Y. Y. Zeevi, “Existence conditions for discrete noncanonical multiwindow Gabor schemes,” IEEE Transactions on Signal Processing, vol. 55, no. 10, pp. 5113–5117, 2007. View at Publisher · View at Google Scholar
  7. Y. Z. Li and Q. F. Lian, “Multi-window Gabor frames and oblique Gabor duals on discrete periodic sets,” Science China, vol. 54, no. 5, pp. 987–1010, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. J. P. Gabardo and Y. Z. Li, “Density results for Gabor systems associated with periodic subsets of the real line,” Journal of Approximation Theory, vol. 157, no. 2, pp. 172–192, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. Q. F. Lian and Y. Z. Li, “Gabor frame sets for subspaces,” Advances in Computational Mathematics, vol. 34, no. 4, pp. 391–411, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. A. Ron and Z. W. Shen, “Frames and stable bases for shift-invariant subspaces of L2(Rd),” Canadian Journal of Mathematics, vol. 47, no. 5, pp. 1051–1094, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. O. Christensen, An Introduction to Frames and Riesz Bases, Birkhäuser, Boston, Mass, USA, 2003.
  12. O. Christensen, Frames and Bases an Introductory Course, Birkhäuser, Boston, Mass, USA, 2008. View at Publisher · View at Google Scholar