Advertisement

On the Development of an Alternative Proposition of Cross Wavelet Analysis for Transient Discrimination Problems

  • Adalberto SchuckJr.
  • Bardo E. J. BodmannEmail author
Chapter

Abstract

This work presents the classical definitions of Cross Wavelet Analysis and proposes new definitions for Wavelet Power Spectrum, Wavelet Cross Spectrum and Wavelet Coherence in a similar way as the Wiener-Khintchine relations to solve shortcomings of the traditional definitions for detecting non-synchronized transients in a Gaussian noise. A detection problem is proposed with simulated signals and both definitions are used for signal analysis. A comparison between the results is then presented, pointing out the aspects of each technique and finally shows that the new definition identifies the transients.

References

  1. [AnEtAl04]
    Antoine, J-P., Murenzi, R., Vandergheynst, P., and Ali, S.T.: Two-Dimensional Wavelets and their Relatives. Cambridge University Press, Cambridge (UK), 2004.CrossRefGoogle Scholar
  2. [BePi00]
    Bendat, J.S., and Piersol, A.G.: Random Data: analysis and measurement procedures. John Wiley and Sons, Inc., 3rd edition, 2000.Google Scholar
  3. [Da92]
    Daubechies, I.: Ten Lectures on Wavelets. SIAM, Philadelphia, 1992.CrossRefGoogle Scholar
  4. [Nt10]
    Ntirwihisha, E.-E.: Corrélation des transformées en ondelettes et ondes sismiques. PhD thesis, Université Catholique de Louvain, Louvain-la-Neuve, BE, 2010.Google Scholar
  5. [GrEtAl04]
    Grinsted, A., Moore, J.C., and Jevrejeva, S.: Application of cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics, 11, 561–566 (2004).CrossRefGoogle Scholar
  6. [HeEtAl05]
    Herrmann, C.S., Grigutsch, M., and Bush, N.A.: EEG oscillations and wavelet analysis. In Event-related potentials: A methods handbook. L.L. Schumaker (Editor), MIT Press, Cambridge, MA, USA, 2005.Google Scholar
  7. [HuEtAl93]
    Hudgins, L., Friehe, C.A., and Mayer, M.E.: Wavelet transforms and atmospheric turbulence. Physical Review Letters, 71(20), 3279–3282 (1993).CrossRefGoogle Scholar
  8. [KlEtAl06]
    Klein, A., Sauer, T., Jedynak, A., and Skrandies, W.: Conventional and wavelet coherence applied to sensory-evoked electrical brain activity. IEEE Transactions on Biomedical Engineering, 53(2), 266–271 (2006).CrossRefGoogle Scholar
  9. [LaEtAl02]
    Lachaux, J.-P., Lutz, A., Rudrauf, D., Cosmelli, D., Le Van Quyen, M., Martinerie, J., and Varela, F.: Estimating the time-course of coherence between single-trial brain signals: An introduction to wavelet coherence. Neurophysiol. Clin., 32, 2002.CrossRefGoogle Scholar
  10. [Li94]
    Liu, P.C.: Wavelet spectrum analysis and ocean wind waves. In Wavelets in Geophysics. E. Foufoula and P.Kumar (Editors), Academic Press, San Diego, CA, USA, 1995.Google Scholar
  11. [MaKu04]
    Maraum, D., and Kurths, J.: Cross wavelet analysis: significance testing and pitfalls. Nonlinear Processes in Geophysics, 11, 505–514 (2004).CrossRefGoogle Scholar
  12. [MaEtAl07]
    Maraum, D., Kurths, J., and Holschneider, M.: Nonstationary gaussian processes in wavelet domain: Synthesis, estimation and significance testing. Physical Review, E75, 016707–1–016707–14 (2007).Google Scholar
  13. [Pl07]
    Plett, M.I.: Transient detection with cross wavelet transforms and wavelet coherence. IEEE Transactions on Signal Processing, 55(5), 1605–1611 (2007).MathSciNetCrossRefGoogle Scholar
  14. [RiFl92]
    Rioul, O., and Flandrin, P.: Time-scale energy distributions: A general class extending wavelet transforms. IEEE Transactions on Signal Processing, 40(07), 1746–1757 (1992).CrossRefGoogle Scholar
  15. [ScEtAl13]
    Schuck Jr., A., Balbinot, A., Zabadal, J.R., and Bodmann, B.E.J.: Alternative propositions of cross wavelet analysis for use in a transient detection problem. International Review of Chemical Engineering I.R.E.C.H.E., 05(6), 1–6 (2013).Google Scholar
  16. [ToCo98]
    Torrence, C. and Compo, G.P.: A practical guide to wavelet analysis. Buletin of the American Meteorological Society, 79(1), 61–78 (1998).CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Electrical Engineering Department (DELET)UFRGSPorto AlegreBrazil
  2. 2.Mechanical Engineering Department (DEMEC)(UFRGS)Porto AlegreBrazil

Personalised recommendations