Advertisement

Wavelets pp 132-138 | Cite as

Wavelet Transformations in Signal Detection

  • F. B. Tuteur
Conference paper
Part of the inverse problems and theoretical imaging book series (IPTI)

Abstract

A new method for dealing with transient signals has recently appeared in the literature [2–11]. The basis functions are referred to as wavelets, and they employ time compression (or dilation) rather than a variation of frequency of the modulated sinusoid. Hence all the wavelets have the same number of cycles. The analyzing wavelets must satisfy a few simple conditions, but are not otherwise specified. There is therefore a wide latitude in the choice of these functions and they can be taylored to specific applications. We have applied them to detect ventricular delayed potentials (VLP) in the el echocardiogram.

Keywords

Discrete Wavelet Transform Analyze Wavelet Wavelet Function Matched Filter Gabor Wavelet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Gabor, “Theory of Communications,” J. IEE, vol. 93 (3), (1946), pp 429–457.Google Scholar
  2. 2.
    A. Grossman and J. Morlet, “Decomposition of Functions into Wavelets of Constant Shape, and Related Transforms.” Center for Interdisciplinary Research and Research Center Bielefeld-Bochum- Stochastics, University of Bielefeld, Report No. 11, December 1984. Also in “Mathematics and Physics 2,” L. Streit, editor, World Scientific Publishing Co., Singapore.Google Scholar
  3. 3.
    P. Goupillaud, A. Grossman, and J. Morlet, “Cycle-Octave and Related Transforms in Seismic Signal Analysis,” Geoexploration 23, 85 (1984/85)CrossRefGoogle Scholar
  4. 4.
    A. Grossman, J. Morlet, T. Paul, “Transforms associated to square-integrable group representations, I: General Results. J. Math. Phys 26 2473, (1985).CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    A. Grossman, J. Morlet, T. Paul, “Transforms associated to square-integrab1e group representations, II: Examples. Ann. Inst. H. Poincare 45 293 (1986).Google Scholar
  6. 6.
    I. Daubechies, A. Grossman, Y. Meyer, “Painless nonorthogona1 expansions”, J.Math. Phys. 27 p1271f (1986),Google Scholar
  7. 7.
    A. Grossman and J. Morlet, “Decomposition of Hardy functions into square integrable wavelets of constant shape”, SIAM J. Math. Anal. 15, p. 723, (1984).Google Scholar
  8. 8.
    R. Kronland-Martinet, J. Morlet, A. Grossman “Analysis of Sound Patterns through Wavelet Transforms.” To appear in International Journal of Pattern Recognition and Artificial Intelligence, Special Issue on Expert Systems and Pattern Analysis.Google Scholar
  9. 9.
    S. Mallat, “A Theory for Multiscale Decompositions The Scale Change Representation,” Grasp Laboratory, Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA 19104–6389 (1986).Google Scholar
  10. 10.
    R.R.Coifrnan and Y, Meyer, “The discrete Wavelet Transform”, Preprint, Yale University Department of Mathematics, 1987.Google Scholar
  11. 11.
    Y. Meyer, S. Jaffard, O. Rioul, “L’analyse par ondelettes,” Pour la Science, Sept. 1987, pp 28–37.Google Scholar
  12. 12.
    D. Marr, Vision, W. H Freeman and Company, 1982.Google Scholar
  13. 13.
    A. Papoulis, The Fourier Integral and its AppIications, McGraw-Hill Book Co. Inc., 1962, p64.Google Scholar
  14. 14.
    E.J. Berbari, B.J. Scherlag, R.R. Hope, R.Lazzara,” Recording from the body surface of arrhythmogenic ventricular activity during the SJT segment”. Am. J. Cardiol. 41(4), p697–702, (April, 1978).Google Scholar
  15. 15.
    G. Breithardt and M. Borggrefe, “Pathophysiological mechanisms and clinical significance of ventricular late potentials”. Eur. Heart J. 7(5), pp 364–85, (May, 1986).Google Scholar
  16. 16.
    D. L. Kuchar, C. W. Thoburn, N. L. Samme1, “Prediction of Serious Arrhythmic Events after Myocardial Infarctions Signal- Averaged Electrocardiogram, HoIter Monitoring and Radionuclide Ventriculography,” JACC vol 9., No.3, March 1987, pp 531–8,(Australia).Google Scholar
  17. 17.
    E.S.Gang, T. Peter, M.E.Rosenthal, W.J.Mandel, and Y.Lass, “Detection of Late Potentials on the Surface Electrocardiogram in Unexplained Syncope,” Am. J. Cardiol, vol. 58, Nov. 1986, pp 1014–1020.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • F. B. Tuteur
    • 1
  1. 1.Department of Electrical EngineeringYale UniversityNew HavenUSA

Personalised recommendations