Introduction

  • Agostino Abbate
  • Casimer M. DeCusatis
  • Pankaj K. Das
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

The concept of wavelets has been discussed in the literature for a very long time. It is based on fundamental ideas which were first expressed more than a century ago in a variety of forms. However, it is only recently that significant progress has been made in the application of wavelets to practical problems in signal processing. The wavelet transform has been proposed as a flexible tool for the multiresolution decomposition of continuous time signals. The pioneering work of Daubechies in the early 1980s has shown the linkage between the wavelet and subband transform theories. Since then, there has been an explosion of interest and a flurry of interdisciplinary research and development activities on wavelet and subband transforms, and their applications [Dau90].

Keywords

Radar Convolution Sine Pyramid Geophysics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Abb94]
    A. Abbate, J. Koay, J. Frankel, S.C. Schroeder, and P. Das, Application of Wavelet Transform Signal Processor to Ultrasound, Proc. of the 1994 IEEE International Ultrasonic Symposium, Publ. 94CH3468-6, pp. 1147–1152, 1994.Google Scholar
  2. [Bur83]
    P.J. Burt and E.H. Andelson, The Laplacian pyramid as a compact image code, IEEE Trans. Communications vol. COM-31, pp. 532–540, 1983.CrossRefGoogle Scholar
  3. [Dau90]
    I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inform. Theory, vol. 36, pp. 961–1005, 1990.MathSciNetMATHCrossRefGoogle Scholar
  4. [DeC95]
    C. DeCusatis, J. Koay, D.M. Litynski, and P. Das, The wavelet transform: fundamentals, applications, & implementation using acousto-optic correlators, SPIE Proc. vol. 2643, pp. 17–37, 1995.CrossRefGoogle Scholar
  5. [DeC96]
    C. DeCusatis, A. Abbate, and P. Das, Wavelet Transform Based Image Processing using Acousto-Optics Correlators, Proc. of 1996 SPIE Conf. on Wavelet Applications, vol. 2762, pp. 302–313, 1996.Google Scholar
  6. [Est77]
    D. Estaban and C. Galand, Application of quadrature mirror filters to split band voice coding schemes, Proc. International Conference on Acoutsics, Speech and Signal Processing ICASSP, pp. 191–195, 1977.Google Scholar
  7. [Gro84]
    A. Grossman and J. Morlet, Decomposition of Hardy functions into square integrable wavelets of constant shape, SIAM J. Math. Anal., vol. 15, no. 4, pp. 723–736, 1984.MathSciNetCrossRefGoogle Scholar
  8. [Mal89]
    S. G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation,. IEEE Trans. on Pattern Analys. and Machine Intell., vol. 11m n. 7, pp. 674–693, 1989.CrossRefGoogle Scholar
  9. [Med95a]
    M.J. Medley, G.J. Saulnier, and P.K. Das, The application of wavelet-domain adaptive filtering to spread spectrum Communications, SPIE Proceedings on Wavelet Applications for Dual-Use, vol. 2491, pp. 233–247, 1995.Google Scholar
  10. [Mey93]
    Y. Meyer, Wavelets. Algorithms and Applications, translated by R.D. Ryan, SIAM, Philadelphia, 1993.Google Scholar
  11. [Sch96a]
    P. Schröder, Wavelets in Computer Graphics, Proc. of IEEE, vol. 84, n. 4, pp. 615–625, 1996.CrossRefGoogle Scholar
  12. [Smi84]
    M.J. Smith and T.P. Barnwell III, A procedure for designing exact reconstruction filter banks for tree structured subband coders, Proc. IEEE Intl. Conf. ASSP, pp. 27.1.1–27.1.4, 1984.Google Scholar
  13. [Vai90]
    P.P. Vaidyanathan, Multirate digital filters, filterbanks, polyphase networks and applications: A tutorial, Proc. IEEE vol. 78, pp. 56–93, 1990.CrossRefGoogle Scholar
  14. [Vet86]
    M. Vetterli, Filter banks allowing perfect reconstruction, Signal Process. vol. 10, no. 3, pp. 219–244, 1986.MathSciNetCrossRefGoogle Scholar
  15. [Wor96]
    G.W. Wornell, “Emerging communication,” Proc. IEEE, vol. 84, pp. 586–603,1996.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Agostino Abbate
    • 1
  • Casimer M. DeCusatis
    • 2
  • Pankaj K. Das
    • 3
  1. 1.Panametrics, Inc.WalthamUSA
  2. 2.Department of Electrical Computer EngineeringUniversity of CaliforniaSan Diego La JollaUSA
  3. 3.Department HHLAIBM CorporationPoughkeepsieUSA

Personalised recommendations