Determination of Instantaneous Frequencies of Low Plasma Waves in the Magnetosheath Using Empirical Mode Decomposition (EMD) and Hilbert Transform (HT)
Affiliation(s)
Department of Physics, Akwa Ibom State University, Ikot Akpaden, Nigeria. Department of Physics, University of Uyo, Uyo, Nigeria.
Department of Physics, Akwa Ibom State University, Ikot Akpaden, Nigeria. Department of Physics, University of Uyo, Uyo, Nigeria.
ABSTRACT
The observations of in-situ spacecraft mission in the magnetosheath and a region of thermalized subsonic plasma behind the bow shock reveal a non-linear behaviour of plasma waves. The study of waves and optics in Physics has given the understanding of the effect of many waves coming together to form a wave field or wave packet. The common aspect of such study shows that two or more waves can superimpose constructively or destructively. The sudden high magnetic field data in the magnetosheath displays such possibility of superposition of waves. In this paper, we use the empirical mode decomposition (EMD) and Hilbert transform (HT) techniques to determine the instantaneous frequencies of low frequency plasma waves in the magnetosheath. Our analysis has shown that the turbulent behavior of magnetic field in the magnetosheath within the selected period is due to superposition of waves.
KEYWORDS
Plasma Waves; Instantaneous Frequency; Empirical Mode Decomposition (EMD); Hilbert Transform (HT)
Plasma Waves; Instantaneous Frequency; Empirical Mode Decomposition (EMD); Hilbert Transform (HT)
Cite this paper
E. Nathaniel, N. George and S. Etuk, "Determination of Instantaneous Frequencies of Low Plasma Waves in the Magnetosheath Using Empirical Mode Decomposition (EMD) and Hilbert Transform (HT)," Atmospheric and Climate Sciences, Vol. 3 No. 4, 2013, pp. 576-580. doi: 10.4236/acs.2013.34060.
E. Nathaniel, N. George and S. Etuk, "Determination of Instantaneous Frequencies of Low Plasma Waves in the Magnetosheath Using Empirical Mode Decomposition (EMD) and Hilbert Transform (HT)," Atmospheric and Climate Sciences, Vol. 3 No. 4, 2013, pp. 576-580. doi: 10.4236/acs.2013.34060.
References
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http://dx.doi.org/10.1016/j.ymssp.2005.09.011 [7] E. U. Nathaniel, “Analysis of Low Frequency Plasma Waves in the Turbulent Magnetosheath; Downstream of the Earth’s Bow Shock,” Ph.D Thesis, University of Sussex, 2010. [8] E. Delechelle, J. Lemoine and O. Niang, “Emperical Mode Decomposition: An Analytical Approach for Sifting Process,” IEEE Signal Processing Letters, Vol. 12, No. 11, 2005, pp. 764-767.
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[1] W. Baumjohann and R. A. Treumann, “Basic Space Plasma Physics,” Imperial College Press, London, 1996. [2] M. G. Kivelson and C. T. Russell, “Introduction to Space Physics,” Cambridge University Press, Cambridge, 1995. [3] B. Boashash, “Estimating and Interpreting the Instantaneous Frequency of a Signal. Part 1: Fundamentals,” Proceedings of the IEEE, Vol. 80, No. 4, 1992, pp. 520-538. http://dx.doi.org/ 10.1109/5.135376 [4] T. Berkant and P. J. Loughlin, “Instantaneous Frequency and Time-Distributions,” Proceedings of the IEEE, Vol. 2, No. 5, 1995, pp. 1013-1016. [5] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, H. H. Liu, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. Yen, C. C. Tung and H. H. Liu, “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis,” Proceedings of the Royal Society of London A, Vol. 454, No. 1971, 1998, pp. 903-995. http://dx.doi.org/10.1098/rspa.1998.0193 [6] J. S. Cheng, D. J. Yu and Y. Yang, “Research on the Intrinsic Mode Function (IMF) Criterion in EMD Method,” Mechanical Systems and Signal Processing, Vol. 20, No. 4, 2006, pp. 817-824.
http://dx.doi.org/10.1016/j.ymssp.2005.09.011 [7] E. U. Nathaniel, “Analysis of Low Frequency Plasma Waves in the Turbulent Magnetosheath; Downstream of the Earth’s Bow Shock,” Ph.D Thesis, University of Sussex, 2010. [8] E. Delechelle, J. Lemoine and O. Niang, “Emperical Mode Decomposition: An Analytical Approach for Sifting Process,” IEEE Signal Processing Letters, Vol. 12, No. 11, 2005, pp. 764-767.
http://dx.doi.org/10.1109/LSP.2005.856878 [9] T. D. Carozzi, A. M. Buckley and M. P. Gough, “Instantaneous Wave-Vector Estimation from Multi-Spacecraft Measurements Using Few Spatial Points,” Annales Geophysicae, Vol. 22, 2004, pp. 2633-2641. http://dx.doi.org/10.5194/angeo-22-2633-2004 [10] L. Cohen, “Time-Frequency Analysis,” Prentice Hall PTR, Upper Saddle River, 1995. [11] R. C. Sharpley and V. Vatchev, “Analysis of the Intrinsic Mode Functions,” Technical Report, Department of Mathematics, University of South Carolina, 2004. [12] P. Flandrin, G. Rilling and P. Goncalves, “Empirical Mode Decomposition as a Filter Bank,” Signal Processing Letters, Vol. 11, No. 2, 2004, pp. 112-114. http://dx.doi.org/10.1109/LSP.2003.821662 [13] N. E. Huang, M. Wu, W. Qu, S. R. Long and S. Shen, “Application of Hilbert-Huang Transform to Non-Stationary Financial Time Series Analysis,” Applied Stochastic Models in Business and Industry, Vol. 19, No. 3, 2003, pp. 245-268. [14] N. Huang, “Hilbert-Huang Transform and Its Applications,” World Scientific Publishing Co. Pte Ltd., Singapore City, 2005. [15] G. Rilling and P. Flandrin, “On the Influence of Sampling on the Empirical Mode Decomposition,” IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 3, Toulouse, 14-19 May 2006, p. 4. [16] E. Bedrosian, “A Product Theorem for Hilbert Transform,” Proceedings of the IEEE, Vol. 51, No. 5, 1963, pp. 868-869. http://dx.doi.org/10.1109/PROC.1963.2308 [17] D. Gabor, “Theory of Communication,” Journal of IEE, Vol. 93, Part III, No. 26, 1946, pp. 429-457. [18] L. Helong, X. Deng and H. Dai, “Structural Damage Detection Using the Combination Method of EMD and Wavelet Analysis,” Mechanical Systems and Signal Processing, Vol. 21, No. 1, 2007, pp. 298-306. http://dx.doi.org/10.1016/j.ymssp.2006.05.001 [19] G. K. Parks, “Physics of Space Plasmas: An Introduction,” Addison-Wesley Publishing Company, Redwood City, 1991.