Abstract
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.
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References
Gabor, D.: Theory of communication. J. Inst. Electron. Eng. 93(11), 429–457 (1946)
Allen, J.B., Rl Rabiner, L.: A unified approach to short–time Fourier analysis and synthesis. Proc. IEEE. 65, 1558–1566 (1977)
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)
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)
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)
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)
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)
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)
Thomson, D.J.: Spectrum estimation and harmonic analysis. Proc. IEEE 70, 1055–1096 (1982)
Bayram, M., Baraniuk, R.G.: Multiple Window Time–Frequency Analysis. In: Proc. IEEE Int. Symp. Time–Frequency and Time–Scale Analysis (May 1996)
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)
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)
Flandrin, P.: Time Frequency/Time Scale Analysis. Academic Press, London (1999)
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)
Boashash, B.: Time frequency signal analysis and processing: a comprehensive reference. Elsevier, London (2003)
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)
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)
Orr, R.: Dimensionality of signal sets. In: Proc. SPIE Int. Soc. Opt. Eng., vol. 1565, pp. 435–446 (1991)
Cohen, L.: What is a multicomponent signal? In: Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing ICASSP 1992, vol. V, pp. 113–116 (1992)
Cohen, L.: Time Frequency Analysis. Prentice–Hall, Englewood Cliffs (1995)
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)
Shannon, C.E.: A mathematical theory of communication, Part I. Bell Sys. Tech. J. 27, 379–423 (1948)
Rényi, A.: On measures of entropy and information. In: Proc. 4th Berkeley Symp. Math. Stat. And Prob., vol. 1, pp. 547–561 (1961)
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Shan, PW., Li, M. (2010). A Study of Nonlinear Time–Varying Spectral Analysis Based on HHT, MODWPT and Multitaper Time–Frequency Reassignment. In: Taniar, D., Gervasi, O., Murgante, B., Pardede, E., Apduhan, B.O. (eds) Computational Science and Its Applications – ICCSA 2010. ICCSA 2010. Lecture Notes in Computer Science, vol 6017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12165-4_16
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DOI: https://doi.org/10.1007/978-3-642-12165-4_16
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