Skip to main content
SpringerLink
Log in

Periodic wavelet frames

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

In this paper, starting from any two functions satisfying some simple conditions, using a periodization method, we construct a dual pair of periodic wavelet frames and show their optimal bounds. The obtained periodic wavelet frames possess trigonometric polynomial expressions. Finally, we present two examples to explain our theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.J. Benedetto and S. Li, The theory of multiresolution analysis frames and applications to filter bands, Appl. Comput. Harmon. Anal. 5 (1998) 389–427.

    Google Scholar 

  2. J.J. Benedetto and O.M. Treiber, Wavelet frame: Multiresolution analysis and extension principle, in: Wavelet Transform and Time-Frequency Signal Analysis, ed. L. Debnath (Birkhäuser, Boston, 2000).

    Google Scholar 

  3. P.G. Casazza and O. Christensen, Weyl–Heisenberg frames for subspaces of L2(R), Proc. Amer. Math. Soc. 129 (2001) 145–154.

    Google Scholar 

  4. O. Christensen, Frames, Riesz bases, and discrete Gabor/wavelet expansions, Bull. Amer. Math. Soc. 38 (2001) 273–291.

    Google Scholar 

  5. C.K. Chui, An Introduction to Wavelets (Academic Press, Boston, 1992).

    Google Scholar 

  6. C.K. Chui and X.L. Shi, Orthonormal wavelets and tight frames with arbitrary real dilations, Appl. Comput. Harmon. Anal. 9 (2000) 243–264.

    Google Scholar 

  7. I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inform. Theory 36 (1990) 961–1005.

    Google Scholar 

  8. I. Daubechies, Ten Lectures on Wavelets, CBMS–NSF Conferences in Applied Mathematics, CBMS Conference Lecture Notes (SIAM, Philadelphia, 1992).

    Google Scholar 

  9. R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Sci. 72 (1952) 341–366.

    Google Scholar 

  10. M. Frazier, G. Garrigos, K.C. Wang, and G. Weiss, A characterization of functions that generate wavelet and related expansion, J. Fourier Anal. Appl. 3 (1997) 883–906.

    Google Scholar 

  11. C. Heil and D. Walnut, Continuous and discrete wavelet transforms, SIAM Rev. 31 (1989) 628–666.

    Google Scholar 

  12. H.O. Kim and J.K. Lim, On frame wavelets associated with frame multiresolution analysis, Appl. Comput. Harmon. Anal. 10 (2001) 61–70.

    Google Scholar 

  13. R.L. Long, Multidimensional Wavelet Analysis (Springer, Beijing, 1995).

    Google Scholar 

  14. R.L. Long and W. Chen, Wavelet basis packets and wavelet frame packets, J. Fourier Anal. Appl. 3 (1997) 239–256.

    Google Scholar 

  15. Y. Meyer, Ondelettes et Operaturs (Hermann, Paris, 1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Chinese Academy of Sciences, Beijing, P.R. China, 100080

    Zhihua Zhang

Authors
  1. Zhihua Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhihua Zhang.

Additional information

Communicated by J.J. Benedetto

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Z. Periodic wavelet frames. Adv Comput Math 22, 165–180 (2005). https://doi.org/10.1007/s10444-004-3139-z

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10444-004-3139-z

Keywords

Search

Navigation