Skip to main content

Wavelet Fundamentals

  • Chapter
Book cover Wavelets and Subbands

Abstract

Signal processing is based on transforming a signal in a manner that it is more useful to the application at hand [Pro88]. For example, if we are interested at reducing the noise in a signal, the best representation is the one in which the signal and noise are easily separated/ The various signal processing techniques described in this book are pictured in Figure 2.1.1.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Abbate, M. Doxbeck, and P. Das, Applications of wavelet transform in signal processing, Proc. of the International Conference on Signal Processing Applications and Technology, pp. 652–655, 1995.

    Google Scholar 

  2. A. Abbate, Wavelet transform applied to ultrasonics, US Army Tech. Rep. ARCCB-TR-95013, 1995.

    Google Scholar 

  3. A. Abbate, J. Frankel, R.W. Reed, and P. Das, Ultrasonic gauging and wavelet image processing for wear and erosion mapping, Proc. of the 1996 QNDE, vol. 18, 1996.

    Google Scholar 

  4. A. Abbate, J. Frankel, and P. Das, Application of wavelet image processing for ultrasonic gaging, Proc. 1997 SPIE Conference on Wavelets, 1997.

    Google Scholar 

  5. A. N. Akansu and R.A. Haddad, Multiresolütion Signal Decomposition Transforms, Subbands, Wavelets, Academic Press, New York, 1994.

    Google Scholar 

  6. A.N. Akansu and M.J. Medley Eds., Wavelet, Subband and Block Transforms in Communications and Multimedia, Kluwer, Boston, 1999.

    MATH  Google Scholar 

  7. C.K. Chui, An Introduction to Wavelets, Academic Press, New York, 1992.

    MATH  Google Scholar 

  8. C.K. Chui, Wavelets: Theory, Algorithms, and Applications, Academic Press, New York, 1995.

    Google Scholar 

  9. L. Cohen, Time-frequency distributions — A review, Proc. IEEE, vol. 77 no. 7, pp. 941–981, 1989.

    Article  Google Scholar 

  10. L. Cohen, The scale representation, IEEE Trans. Signal Process., vol. 41, pp. 3275–3292, 1993.

    Article  MATH  Google Scholar 

  11. A. Cohen and J. Kovacevic, Wavelets: The mathematical background, Proc. IEEE, vol. 84, no. 4, pp. 514–522, 1996.

    Article  Google Scholar 

  12. P. Das and C. DeCusatis, A review of acousto-optic image correlators, Proc. SPIE 5th Annual School Seminar on Acousto-optics and Applications, vol. 1844, pp. 33–48, 1993.

    Google Scholar 

  13. I. Daubeches and J. Lagarias, Two scale differential equations, 11 local regularity, infinite products of matricies, and fractals, AT&T Bell Labs Tech. Report, 1989.

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  15. I. Daubechies, The wavelet transform: a method for time-frequency localization, in Advances in Spectrum Analysis and Array Processing, vol. 1, edited by S. Haykins, Prentice-Hall, Englewood Cliffs, NJ, pp. 366–417, 1991.

    Google Scholar 

  16. I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.

    Book  MATH  Google Scholar 

  17. C. DeCusatis, P. Das, and J. Koay, Perfect reconstruction wavelets using acousto-optic correlators, Proc. OSA Annual Meeting, 1994.

    Google Scholar 

  18. C. DeCusatis, A. Abbate, and P. Das, Wavelet transform based image processing using acousto-optics correlators, Proc. of J 996 SPIE Conf. on Wavelet Applications, vol. 2762, pp. 302–313, 1996.

    Google Scholar 

  19. C. DeCusatis, A. Abbate, D.M. Litynski, and P. Das, Wavelet image processing for optical pattern recognition and feature extraction, SPIE Proc., vol. 3110, pp. 804–815, 1997.

    Article  Google Scholar 

  20. C. DeCusatis, A. Abbate, and P. Das, Progressive pattern recognition using the wavelet transform, Int. J. Optoelectron., vol. 11, p. 425–432, 1997.

    Google Scholar 

  21. D.E. Dudgeon and R.M. Mersereau, Multidimensional Digital Signal Processing, Prentice-Hall, Englewoods Cliffs, NJ, 1984.

    MATH  Google Scholar 

  22. P. Goupillaud, A. Grossmann and J. Morlet, Cycle-octave and related transforms in seismic signal analysis, Geoexploration, vol. 23, pp. 85–102, 1984.

    Article  Google Scholar 

  23. 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 

  24. A. Grossmann, M. Holschneider, R. Kronland-Martinet, and J. Morlet, Detection of abrupt changes in sound signals with the help of wavelet transforms, in Inverse Problems, Academic Press, New York, pp. 289–306, 1987.

    Google Scholar 

  25. S. G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans, on Pattern Analys. and Machine Intell., vol. 11, no. 7, pp. 674–693, 1989.

    Article  MATH  Google Scholar 

  26. J.G. Proakis and D.G. Manolakis, Introduction to Digital Signal Processing, Macmillan, New York, 1988.

    Google Scholar 

  27. L.R. Rabiner and R.W. Schafer, Digital Signal Processing of Speech Signals, Prentice-Hall, Englewwod Cliffs, NJ, 1978.

    Google Scholar 

  28. O. Rioul, A discrete-time multiresolution theory, IEEE Trans. Signal Process., vol. 41 no. 8, pp. 1606–2591, 1993.

    Article  Google Scholar 

  29. B.L. Shoop, A.H. Sayles, G.P. Dudevoir, D.A. Hall, D.M. Litynski, and P. K. Das, Smart pixel based wavelet transformation for wideband radar and sonar signal processing, SPIE Proc, vol. 3078, pp. 415–423, 1997.

    Article  Google Scholar 

  30. G. Strang, Wavelets and dilation equation: A brief introduction, SIAM Rev., vol. 31, pp. 614–627, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  31. G. Strang, Wavelets, American Scientist, vol. 82, pp. 250–255, 1994.

    Google Scholar 

  32. G. Strang and T. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, Cambridge, 1996.

    Google Scholar 

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

    Article  Google Scholar 

  34. P.P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice-Hall, Englewwod Cliffs, NJ, 1993.

    MATH  Google Scholar 

  35. M. Vetterli, A theory of multirate filter banks, IEEE Trans. Acoust. Speech Signal Process., vol. 35, pp. 356–372, 1987.

    Article  Google Scholar 

  36. M. Vetterli and C. Herley, Wavelets and filter banks: relationships and new results, Proc. ICASSP (Int. confon acoustics, speech, and signal processing), vol. 3, pp. 1723–1726, 1990.

    Google Scholar 

  37. M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice-Hall, Englewood Cliffs, NJ, 1995.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media New York

About this chapter

Cite this chapter

Abbate, A., DeCusatis, C.M., Das, P.K. (2002). Wavelet Fundamentals. In: Wavelets and Subbands. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0113-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0113-7_2

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6618-1

  • Online ISBN: 978-1-4612-0113-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics