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Time-Time Distributions for Discrete Wavelet Transforms

  • C. R. Pinnegar
  • H. Khosravani
  • P. Federico
Part of the Operator Theory: Advances and Applications book series (OT, volume 205)

Abstract

The short-time Fourier transform has an easily defined time-domain counterpart: a set of windowed time series, each one corresponding to a specific window position. Considered collectively, these constitute a time-time distribution, since the window position gives a second time variable. Multiresolution time-time distributions can also be defined. The only such distribution that has been investigated thus far, the TT-transform, is the time-domain counterpart of a continuous wavelet transform. In this short paper, we describe a new method of calculating time-time distributions for discrete wavelet transforms, and present two examples.

Keywords

Short-time Fourier transform time-time distribution TT-transform wavelet transform 

Mathematics Subject Classification (2000)

Primary 65T60 Secondary 47G30 

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References

  1. [1]
    L. Cohen, Time-Frequency Analysis, Prentice-Hall, 1995.Google Scholar
  2. [2]
    X. Fan and M. J. Zuo, Gearbox fault detection using Hilbert and TT-transform, Key Engineering Materials 293–294 (2005), 79–86.CrossRefGoogle Scholar
  3. [3]
    P. C. Gibson, M. P. Lamoureux and G. F. Margrave, Letter to the editor: Stockwell and wavelet transforms. J. Fourier Anal. Appl. 12 (2006) 713–721.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    K. Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser, 2001.Google Scholar
  5. [5]
    S. Mallat, A Wavelet Tour of Signal Processing, Second Edition, Academic Press, 1999.Google Scholar
  6. [6]
    C. R. Pinnegar, Time-frequency and time-time filtering with the S-transform and TT-transform, Dig. Signal Process 15 (2005), 604–620.CrossRefGoogle Scholar
  7. [7]
    C. R. Pinnegar and L. Mansinha, A method of time-time analysis: The TT-transform, Dig. Signal Process. 13 (2003) 588–603.CrossRefGoogle Scholar
  8. [8]
    C. R. Pinnegar, M. W. Wong, and H. Zhu, Integral representations of the TT-transform, App. Anal. 85 (2006) 933–940.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    R. G. Stockwell, L. Mansinha, and R. P. Lowe, Localization of the complex spectrum: The S-transform, IEEE Trans. Signal Process. 44 (1996) 998–1001.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • C. R. Pinnegar
    • 1
  • H. Khosravani
    • 1
  • P. Federico
    • 1
  1. 1.Department of Clinical NeurosciencesUniversity of Calgary Foothills Medical CentreCalgaryCanada

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