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Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 618231, 14 pages
http://dx.doi.org/10.1155/2010/618231
Research Article

Nonlinear Time-Varying Spectral Analysis: HHT and MODWPT

School of Information Science & Technology, East Normal University, No. 500, Dong—Chuan Road, Shanghai 200241, China

Received 31 January 2010; Accepted 19 March 2010

Academic Editor: Cristian Toma

Copyright © 2010 Pei-Wei Shan and Ming Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Li, X. K Gu, and P. W Shan, “Time-frequency distribution of encountered waves using Hilbert-Huang transform,” International Journal of Mechanics, vol. 1, no. 2, pp. 27–32, 2007. View at Google Scholar
  2. P. Flandrin, Time-Frequency/Time-Scale Analysis, vol. 10 of Wavelet Analysis and Its Applications, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
  3. H. Tong, Nonlinear Time Series Analysis, Oxford University Press, Oxford, UK, 1990.
  4. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis, vol. 7 of Cambridge Nonlinear Science Series, Cambridge University Press, Cambridge, UK, 1997. View at MathSciNet
  5. C. Diks, Nonlinear Time Series Analysis, vol. 4 of Nonlinear Time Series and Chaos, World Scientific, Singapore, 1999. View at MathSciNet
  6. N. E. Huang and S. S. Shen, Eds., Hilbert-Huang Transform and Its Applications, vol. 5 of Interdisciplinary Mathematical Sciences, World Scientific, Singapore, 2005. View at MathSciNet
  7. N. E. Huang, Z. Shen, S. R. Long et al., “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Society London A, vol. 454, no. 1971, pp. 903–995, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. P. Flandrin and P. Gonçalvès, “Empirical mode decompositions as data-driven wavelet-like expansions,” International Journal of Wavelets, Multiresolution and Information Processing, vol. 2, no. 4, pp. 477–496, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. P. Shan and M. Li, “An EMD based simulation of fractional Gaussian noise,” International Journal of Mathematics and Computers in Simulation, vol. 1, no. 4, pp. 312–316, 2007. View at Google Scholar
  10. N. E. Huang, S. R. Long, and C. C. Tung, “The local properties of transient stochastic data by the phase-time method,” in Computational Methods for Stochastic Processes, pp. 253–279, 1993. View at Google Scholar
  11. W. Huang, Z. Shen, N. E. Huang, and Y. C. Fung, “Engineering analysis of biological variables: an example of blood pressure over 1 day,” Proceedings of the National Academy of Sciences of the United States of America, vol. 95, no. 9, pp. 4816–4821, 1998. View at Publisher · View at Google Scholar · View at Scopus
  12. N. E. Huang, “Nonlinear evolution of water waves: Hilbert's view,” in Proceedings of the International Symposium on Experimental Chaos, W. Ditto, C. Grebogi, E. Ott et al., Eds., pp. 327–341, World Scientific, Scotland, UK, 2nd edition, 1995. View at Google Scholar
  13. M. Datig and T. Schlurmann, “Performance and limitations of the Hilbert-Huang transformation (HHT) with an application to irregular water waves,” Ocean Engineering, vol. 31, no. 14, pp. 1783–1834, 2004. View at Publisher · View at Google Scholar · View at Scopus
  14. N. E. Huang and Z. H. Wu, “A review on Hilbert-Huang transform: method and its applications to geophysical studies,” Reviews of Geophysics, vol. 46, no. 2, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. C. Cattani and J. Rushchitsky, Wavelet and Wave Analysis as Applied to Materials with Micro or Nanostructure, vol. 74 of Series on Advances in Mathematics for Applied Sciences, World Scientific, Singapore, 2007. View at MathSciNet
  16. C. Cattani, “Harmonic wavelet approximation of random, fractal and high frequency signals,” Telecommunication Systems, vol. 43, no. 3-4, pp. 207–217, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. C. Cattani, “Harmonic wavelet analysis of a localized fractal,” International Journal of Engineering and Interdisciplinary Mathematics, vol. 1, no. 1, pp. 35–44, 2009. View at Google Scholar
  18. C. Cattani, “Shannon wavelets theory,” Mathematical Problems in Engineering, vol. 2008, Article ID 164808, 24 pages, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. C. L. Zhang, H. Chen, X. F. Wang, and D.-H. Fan, “Harmonic wavelet analysis of a localized parabolic partial differential equation,” International Journal of Engineering and Interdisciplinary Mathematics, vol. 1, no. 1, pp. 45–55, 2009. View at Google Scholar
  20. W.-S. Chen, “Galerkin-Shannon of Debye's wavelet method for numerical solutions to the natural integral equations,” International Journal of Engineering and Interdisciplinary Mathematics, vol. 1, no. 1, pp. 63–73, 2009. View at Google Scholar
  21. A. T. Walden and A. Contreras Cristan, “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, vol. 454, no. 1976, pp. 2243–2266, 1998. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. E. Tsakiroglou and A. T. Walden, “From Blackman—Tukey pilot estimators to wavelet packet estimators: a modern perspective on an old spectrum estimation idea,” Signal Processing, vol. 82, no. 10, pp. 1425–1441, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  23. M. Li and S. C. Lim, “Modeling network traffic using generalized Cauchy process,” Physica A, vol. 387, no. 11, pp. 2584–2594, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. M. Li, “Fractal time series—a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  25. M. Li and W. Zhao, “Representation of a stochastic traffic bound,” IEEE Transactions on Parallel and Distributed Systems. In press.
  26. M. Li and W. Zhao, “Variance bound of ACF estimation of one block of fGn with LRD,” Mathematical Problems in Engineering, vol. 2010, Article ID 560429, 14 pages, 2010. View at Publisher · View at Google Scholar
  27. M. Li and P. Borgnat, “Foreword to the special issue on traffic modeling, its computations and applications,” Telecommunication Systems, vol. 43, no. 3-4, pp. 145–146, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. M. Li, W.-S. Chen, and L. Han, “Correlation matching method for the weak stationarity test of LRD traffic,” Telecommunication Systems, vol. 43, no. 3-4, pp. 181–195, 2010. View at Google Scholar
  29. M. Li and S. C. Lim, “Power spectrum of generalized Cauchy process,” Telecommunication Systems, vol. 43, no. 3-4, pp. 291–222, 2010. View at Google Scholar
  30. M. Li, “Recent results on the inverse of min-plus convolution in computer networks,” International Journal of Engineering and Interdisciplinary Mathematics, vol. 1, no. 1, pp. 1–9, 2009. View at Google Scholar
  31. C.-M. Cheng, H. T. Kung, and K.-S. Tan, “Use of spectral analysis in defense against DoS attacks,” in Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM '02), vol. 3, pp. 2143–2148, Taipei, China, 2002. View at Scopus