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Introduction

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Wavelets and Subbands

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].

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References

  1. 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. 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.

    Article  Google Scholar 

  3. I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inform. Theory, vol. 36, pp. 961–1005, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  4. 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.

    Article  Google Scholar 

  5. 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. 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. 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.

    Article  MathSciNet  Google Scholar 

  8. 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.

    Article  Google Scholar 

  9. 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. Y. Meyer, Wavelets. Algorithms and Applications, translated by R.D. Ryan, SIAM, Philadelphia, 1993.

    Google Scholar 

  11. P. Schröder, Wavelets in Computer Graphics, Proc. of IEEE, vol. 84, n. 4, pp. 615–625, 1996.

    Article  Google Scholar 

  12. 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. P.P. Vaidyanathan, Multirate digital filters, filterbanks, polyphase networks and applications: A tutorial, Proc. IEEE vol. 78, pp. 56–93, 1990.

    Article  Google Scholar 

  14. M. Vetterli, Filter banks allowing perfect reconstruction, Signal Process. vol. 10, no. 3, pp. 219–244, 1986.

    Article  MathSciNet  Google Scholar 

  15. G.W. Wornell, “Emerging communication,” Proc. IEEE, vol. 84, pp. 586–603,1996.

    Article  Google Scholar 

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Abbate, A., DeCusatis, C.M., Das, P.K. (2002). Introduction. In: Wavelets and Subbands. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0113-7_1

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  • DOI: https://doi.org/10.1007/978-1-4612-0113-7_1

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6618-1

  • Online ISBN: 978-1-4612-0113-7

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