Skip to main content

Finite-field wavelet transforms

  • Signal Processing and Pattern Recognition
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1133))

Abstract

Cyclic wavelet transforms, analogous to cyclic Fourier transforms, are described. Among other things, this construction allows for the development of wavelet transforms over finite fields. Potential applications of this construct in algebraic coding are discussed.

This paper was prepared under the support of the U. S. Office of Naval Research under Grant N00014-94-1-0115.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. C. Benson, “Digital signal processing methods for biosequence analysis,” Nucleic Acids Research, vol. 18, no. 10, pp. 3001–3006, 1990.

    Google Scholar 

  2. R. E. Blahut, Theory and Practice of Error Control Codes. Addison-Wesley, Reading, MA, 1983.

    Google Scholar 

  3. R. E. Blahut, Fast Algorithms for Digital Signal Processing. Addison-Wesley, Reading, MA, 1984.

    Google Scholar 

  4. G. Caire, R. L. Grossman and H. V. Poor, “Wavelet transforms associated with finite cyclic groups,” IEEE Trans. Inform. Theory, Vol. 37, No. 5, pp. 1157–1166, July 1993.

    Google Scholar 

  5. I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Comm. Pure Appl. Math., Vol. 41, pp. 909–996, 1988.

    Google Scholar 

  6. I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inform. Theory, Vol. 36, pp. 961–1005, Sept. 1990.

    Google Scholar 

  7. P. J. Davis, Circulant Matrices (Wiley, New York, 1979)

    Google Scholar 

  8. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-correcting Codes. (North-Holland: New York, 1977)

    Google Scholar 

  9. S. G. Mallat, “A theory of multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Anal. Machine Intell., Vol. 11, pp. 674–693, 1989.

    Google Scholar 

  10. D. Pollen, “SU I (2, F[z, 1/z]) for F a subfield of C,” J. Am. Math. Soc, Vol. 3, pp. 611–624, July 1990.

    Google Scholar 

  11. S. Sarkar and H. V. Poor, “Certain generalizations of the cyclic wavelet transform,” Proc. 1995 Conf. Inform. Sci. Syst., The Johns Hopkins University, Mar. 22–24, 1995.

    Google Scholar 

  12. S. Sarkar and H. V. Poor, “Finite-field wavelet transforms and multilevel error protection,” Proc. 1995 IEEE Int'l Symp. Inform. Theory, Whistler, BC, Sept. 17–22, 1995.

    Google Scholar 

  13. S. Sarkar and H. V. Poor, “Multilevel error protection: A wavelet transform approach to coding,” preprint, January 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jean-Yves Chouinard Paul Fortier T. Aaron Gulliver

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Poor, H.V. (1996). Finite-field wavelet transforms. In: Chouinard, JY., Fortier, P., Gulliver, T.A. (eds) Information Theory and Applications II. CWIT 1995. Lecture Notes in Computer Science, vol 1133. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0025146

Download citation

  • DOI: https://doi.org/10.1007/BFb0025146

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61748-8

  • Online ISBN: 978-3-540-70647-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics