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Alternative Time–Frequency Representations

  • Sean A. FulopEmail author
Chapter
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Part of the Signals and Communication Technology book series (SCT)

Abstract

The spectrogram is a well-studied time–frequency representation, but there are numerous others. There has been a rich literature on this subject, and many different time–frequency representations have been devised, studied, and applied to various signal analysis problems (e.g. [1]). Unfortunately, the subject has never to my knowledge been made accessible to speech scientists, with the result that we have rarely availed ourselves of any such representations other than the spectrogram. This chapter is an attempt to rectify this situation somewhat, although the presentation takes on a more advanced mathematical character at certain points.

Keywords

Speech Signal Instantaneous Frequency Frequency Localization Linear Frequency Modulation Frequency Representation 
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.

References

  1. 1.
    M. Akay (ed.), Time Frequency and Wavelets in Biomedical Signal Processing (IEEE Press, Piscataway, 1998)Google Scholar
  2. 2.
    M.G. Amin, Time and lag window selection in Wigner–Ville distribution, in Proceedings of the International Conference on Acoustics, Speech and Signal Processing (IEEE, New York, 1987), pp. 1529–1532Google Scholar
  3. 3.
    L.E. Atlas, P.J. Loughlin, J.W. Pitton, Signal analysis with cone kernel time–frequency distributions and their application to speech, in Time–Frequency Signal Analysis: Methods and Applications, Chap.16, ed. by B. Boashash (Halsted Press, New York, 1992)Google Scholar
  4. 4.
    F. Auger, P. Flandrin, P. Gonçalvès, O. Lemoine, Time–Frequency Toolbox Reference Guide (1996)Google Scholar
  5. 5.
    B. Boashash, Heuristic formulation of time–frequency distributions, in Time Frequency Signal Analysis and Processing, Chap. 2, ed. by B. Boashash (Elsevier, Amsterdam, 2003)Google Scholar
  6. 6.
    B. Boashash, Theory of quadratic TFDs, in Time Frequency Signal Analysis and Processing, Chap. 3, ed. by B. Boashash (Elsevier, Amsterdam, 2003)Google Scholar
  7. 7.
    B. Boashash, G.R. Putland, Computation of discrete quadratic TFDs, in Time Frequency Signal Analysis and Processing, Chap. 6.5, ed. by B. Boashash (Elsevier, Amsterdam, 2003)Google Scholar
  8. 8.
    B. Boashash, G.R. Putland, Discrete time–frequency distributions, in Time Frequency Signal Analysis and Processing, Chap. 6.1, ed. by B. Boashash (Elsevier, Amsterdam, 2003)Google Scholar
  9. 9.
    B. Boashash, L. White, J. Imberger, Wigner–Ville analysis of non-stationary random signals, in Proceedings of the International Conference on Acoustics, Speech and Signal Processing (IEEE, New York, 1986), pp. 2323–2326Google Scholar
  10. 10.
    T.A.C.M. Claasen, W.F.G. Mecklenbräuker, The Wigner distribution—a tool for time–frequency signal analysis, part II: discrete-time signals. Philips J. Res. 35(4/5), 276–300 (1980)MathSciNetzbMATHGoogle Scholar
  11. 11.
    L. Cohen, Generalized phase-space distribution functions. J. Math. Phys. 7(5), 781–786 (1966)CrossRefGoogle Scholar
  12. 12.
    P. Flandrin, Time–Frequency/Time-Scale Analysis, English edn. (Academic Press, San Diego, 1999)Google Scholar
  13. 13.
    K. Gröchenig, Foundations of Time–Frequency Analysis (Birkhäuser, Boston, 2001)zbMATHGoogle Scholar
  14. 14.
    F. Hlawatsch, T.G. Manickam, R.L. Urbanke, W. Jones, Smoothed pseudo-Wigner distribution, Choi–Williams distribution, and cone-kernel representation: ambiguity-domain analysis and experimental comparison. Signal Process. 43, 149–168 (1995)zbMATHCrossRefGoogle Scholar
  15. 15.
    S. Kadambe, G.F. Boudreaux-Bartels, A comparison of the existence of “cross-terms” in the Wigner distribution and the squared magnitude of the wavelet transform and the short time Fourier transform. IEEE Trans. Signal Process. 40(10), 2498–2517 (1992)zbMATHCrossRefGoogle Scholar
  16. 16.
    P.J. Loughlin, J.W. Pitton, L.E. Atlas, Bilinear time–frequency representations: new insights and properties. IEEE Trans. Signal Process. 41(2), 750–767 (1993)zbMATHCrossRefGoogle Scholar
  17. 17.
    W. Martin, P. Flandrin, Wigner–Ville spectral analysis of nonstationary processes. IEEE Trans. Acoust. Speech Signal Process. 33(6), 1461–1470 (1985)CrossRefGoogle Scholar
  18. 18.
    J.M. O’Toole, M. Mesbah, B. Boashash, A new discrete analytic signal for reducing aliasing in the discrete Wigner–Ville distribution. IEEE Trans. Signal Process. 56(11), 5427–5434 (2008)MathSciNetCrossRefGoogle Scholar
  19. 19.
    J.M. O’Toole, M. Mesbah, B. Boashash, Improved discrete definition of quadratic time–frequency distributions. IEEE Trans. Signal Process. 58(2), 906–911 (2010)MathSciNetCrossRefGoogle Scholar
  20. 20.
    J. Ville, Théorie et applications de la notion de signal analytique. Cables et Transmission 2A(1), 61–77 (1948)Google Scholar
  21. 21.
    E.P. Wigner, On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40(5), 749–759 (1932)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Wikipedia (2009), Convolution. http://www.wikipedia.org
  23. 23.
    Wikipedia (2009), Rectangular function. http://www.wikipedia.org
  24. 24.
    Wikipedia (2009), Sinc function. http://www.wikipedia.org
  25. 25.
    Y. Zhao, L.E. Atlas, R.J. Marks II, The use of cone-shaped kernels for generalized time–frequency representations of nonstationary signals. IEEE Trans. Acoust. Speech Signal Process. 38(7), 1084–1091 (1990)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of LinguisticsCalifornia State University FresnoFresnoUSA

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