A Study of Nonlinear Time–Varying Spectral Analysis Based on HHT, MODWPT and Multitaper Time–Frequency Reassignment

  • Pei-Wei Shan
  • Ming Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6017)


Numerous approaches have been explored to improve the performance of time–frequency analysis and to provide a sufficiently clear time–frequency representation. Among them, three methods such as the empirical mode decomposition (EMD) with Hilbert transform (HT) (or termed as the Hilbert–Huang Transform (HHT)), along with the Hilbert spectrum based on maximal overlap discrete wavelet package transform (MODWPT) and the multitaper time–frequency reassignment raised by Xiao and Flandrin, are noteworthy. This study evaluates the performances of three transforms mentioned above, in estimating single and multicomponent chip signals in the presence of noise or noise–free. Rényi Enropy is implemented for measuring the effectiveness of each algorithm. The paper demonstrates that under these conditions MODWPT owes better time–frequency resolution and statistical stability than the HHT. The multitaper time–frequency reassigned spectrogram makes excellent trade–off between time–frequency localization and local stationarity.


Hilbert–Huang transform MODWPT Multitaper Time–frequency reassignment Rényi entropy 


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  1. 1.
    Gabor, D.: Theory of communication. J. Inst. Electron. Eng. 93(11), 429–457 (1946)Google Scholar
  2. 2.
    Allen, J.B., Rl Rabiner, L.: A unified approach to short–time Fourier analysis and synthesis. Proc. IEEE. 65, 1558–1566 (1977)CrossRefGoogle Scholar
  3. 3.
    Huang, N.E., Shen, Z., Long, S.R.: A new view of nonlinear water waves: the Hilbert spectrum. Annual Review of Fluid Mechanics 31, 417–457 (1999)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Datig, M., Schlurmann, T.: Performance and limitations of the Hilbert–Huang transformation (HHT) with an application to irregular water waves. Ocean Engineering 31(14), 1783–1834 (2004)CrossRefGoogle Scholar
  5. 5.
    Jingping, Z., Daji, H.: Mirror extending and circular spline function for empirical mode decomposition method. Journal of Zhejiang University (Science) 2(3), 247–252 (2001)CrossRefGoogle Scholar
  6. 6.
    Walden, A.T., Contreras, C.A.: The phase–corrected undecimated discrete wavelet packet transform and its application to interpreting the timing of events. Proceedings of the Royal Society of London Series 454, 2243–2266 (1998)zbMATHCrossRefGoogle Scholar
  7. 7.
    Tsakiroglou, E., Walden, A.T.: From Blackman–Tukey pilot estimators to wavelet packet estimators: a modern perspective on an old spectrum estimation idea. Signal Processing 82, 1425–1441 (2002)zbMATHCrossRefGoogle Scholar
  8. 8.
    Auger, F., Flandrin, P.: Improving the readability of Time–Frequency and Time–Scale representations by the reassignment method. IEEE Transactions on Signal Processing 43(5), 1068–1089 (1995)CrossRefGoogle Scholar
  9. 9.
    Thomson, D.J.: Spectrum estimation and harmonic analysis. Proc. IEEE 70, 1055–1096 (1982)CrossRefGoogle Scholar
  10. 10.
    Bayram, M., Baraniuk, R.G.: Multiple Window Time–Frequency Analysis. In: Proc. IEEE Int. Symp. Time–Frequency and Time–Scale Analysis (May 1996)Google Scholar
  11. 11.
    Xiao, J., Flandrin, P.: Multitaper time–frequency reassignment for nonstationary spectrum estimation and chirp enhancement. IEEE Trans. Sig. Proc. 55(6) (Part 2), 2851–2860 (2007)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Huang, N.E., Shen, Z., Long, S.R., Wu, M.L., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C., Liu, H.H.: The Empirical Mode Decomposition and Hilbert Spectrum for Nonlinear and Non–Stationary Time Series Analysis. Proc. Roy. Soc. London A 454, 903–995 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Flandrin, P.: Time Frequency/Time Scale Analysis. Academic Press, London (1999)zbMATHGoogle Scholar
  14. 14.
    Flandrin, P., Auger, F., Chassande–Mottin, E.: Time Frequency Reassignment From Principles to Algorithms. In: Papandreou–Suppappola, A. (ed.) Applications in Time Frequency Signal Processing, vol. 5, pp. 179–203. CRC Press, Boca Raton (2003)Google Scholar
  15. 15.
    Boashash, B.: Time frequency signal analysis and processing: a comprehensive reference. Elsevier, London (2003)Google Scholar
  16. 16.
    Bayram, M., Baraniuk, R.G.: Multiple window time varying spectrum estimation. In: Fitzgerald, W.J., et al. (eds.) Nonlinear and Nonstationary Signal Processing, pp. 292–316. Cambridge Univ. Press, Cambridge (2000)Google Scholar
  17. 17.
    Williams, W.J., Brown, M.L., Hero, A.O.: Uncertainty, information, and time frequency distributions. In: Proc. SPIE Int. Soc. Opt. Eng., vol. 1566, pp. 144–156 (1991)Google Scholar
  18. 18.
    Orr, R.: Dimensionality of signal sets. In: Proc. SPIE Int. Soc. Opt. Eng., vol. 1565, pp. 435–446 (1991)Google Scholar
  19. 19.
    Cohen, L.: What is a multicomponent signal? In: Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing ICASSP 1992, vol. V, pp. 113–116 (1992)Google Scholar
  20. 20.
    Cohen, L.: Time Frequency Analysis. Prentice–Hall, Englewood Cliffs (1995)Google Scholar
  21. 21.
    Baraniuk, R.G., Flandrin, P., Janssen, A.J.E.M., Michel, O.: Measuring time frequency information content using the Renyi Entropies. IEEE Transactions on Information Theory 47(4), 1391–1409 (2007)CrossRefMathSciNetGoogle Scholar
  22. 22.
    Shannon, C.E.: A mathematical theory of communication, Part I. Bell Sys. Tech. J. 27, 379–423 (1948)zbMATHMathSciNetGoogle Scholar
  23. 23.
    Rényi, A.: On measures of entropy and information. In: Proc. 4th Berkeley Symp. Math. Stat. And Prob., vol. 1, pp. 547–561 (1961)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Pei-Wei Shan
    • 1
  • Ming Li
    • 1
  1. 1.School of Information Science & TechnologyEast Normal UniversityShanghaiChina

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