Signal analysis via instantaneous frequency estimation of signal components

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• 作者：Charles K. Chui ; Maria D. van der Walt
• 关键词：Time–frequency analysis ; Instantaneous frequency ; Empirical mode decomposition ; Intrinsic mode functions ; Synchrosqueezing wavelet transform ; Hilbert transform ; Hilbert spectrum ; Adaptive harmonic model ; Local spline interpolation ; 94A12 ; 41A05 ; 41A15
• 刊名：GEM - International Journal on Geomathematics
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：6
• 期：1
• 页码：1-42
• 全文大小：1,379 KB
• 参考文献：1. Boashash, B (1992) Estimating and interpreting the instantaneous frequency of a signal. i. Fundamentals. Proc. IEEE 80: pp. 520-538 CrossRef
  2. Boashash, B (1992) Estimating and interpreting the instantaneous frequency of a signal. ii. Algorithms and applications. Proc. IEEE 80: pp. 540-568 CrossRef
  3. Carew, JD, Wahba, G, Xie, X, Nordheim, EV, Elizabeth Meyerand, M (2003) Optimal spline smoothing of fmri time series by generalized cross-validation. NeuroImage 18: pp. 950-961 CrossRef
  4. Chen, G, Chui, Charles K, Lai, MJ (1988) Construction of real-time spline quasi-interpolation schemes.. Approx. Theory Appl. 4: pp. 61-75
  5. Chen, Q, Huang, NE, Riemenschneider, S, Xu, Y (2006) A B-spline approach for empirical mode decompositions. Adv. Comput. Math. 24: pp. 171-195 CrossRef
  6. Chen, Y-C, Cheng, M-Y, Wu, H-T (2014) Non-parametric and adaptive modelling of dynamic periodicity and trend with heteroscedastic and dependent errors. J. Roy. Stat. Soc. Ser. B (Stat. Methodol.) 76: pp. 651-682 CrossRef
  7. Chui, C.K., Mhaskar, H.N.: Signal decomposition and analysis via extraction of frequencies. Appl. Comput. Harmon. Anal. (2015). http://dx.doi.org/10.1016/j.acha.2015.01.003
  8. Chui, CK, Diamond, H (1990) A general framework for local interpolation. Numerische Mathematik 58: pp. 569-581 CrossRef
  9. Chui, C.K., Lin, Y.-T., Wu, H.-T.: Real-time dynamics acquisition from irregular samples—with application to anesthesia evaluation. arXiv preprint arXiv:1406.1276 (2014)
  10. Craven, P, Wahba, G (1978) Smoothing noisy data with spline functions. Numerische Mathematik 31: pp. 377-403 CrossRef
  11. Curry, HB, Schoenberg, IJ (1966) On Pólya frequency functions iv: The fundamental spline functions and their limits. Journal d’Analyse Math-matique 17: pp. 71-107 CrossRef
  12. Daubechies, I, Lu, J, Wu, H-T (2011) Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool. Appl. Comput. Harmon. Anal. 30: pp. 243-261 CrossRef
  13. Daubechies, I., Maes, S.: A nonlinear squeezing of the continuous wavelet transform based on auditory nerve models. In: Aldroubi, A., Unser, M.A. (eds.) Wavelets in Medicine and Biology, pp. 527-46. CRC Press, Boca Raton (1996)
  14. de Boor, C.: A Practical Guide to Splines. Applied Mathematical Sciences, vol. 27. Springer, Berlin (2001)
  15. Boor, C, Fix, G (1973) Spline approximation by quasi-interpolants. J. Approx. Theory 8: pp. 96-110
  16. Gabor, D (1946) Theory of communication. J. Inst. Electr. Eng. Part III Radio Commun. Eng. 93: pp. 429-441
  17. Golub, GH, Heath, M, Wahba, G (1979) Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21: pp. 215-223 CrossRef
  18. Heisenberg, W (1927) über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik 43: pp. 172-198 CrossRef
  19. Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.-C., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. Roy. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 454(1971), 903-95 (1998)
  20. Huang, NE, Wu, Z (2008) A review on Hilbert-Huang transform: method and its applications to geophysical studies. Rev. Geophys. 46: pp. 1-23 CrossRef
  21. Kennard, EH (1927) Zur Qu
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Applications of Mathematics
  Computational Science and Engineering
  Mathematical Applications in Earth Sciences
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1869-2680

文摘

The empirical mode decomposition (EMD) algorithm, introduced by Huang et al. (Proc Roy Soc Lond Ser A Math Phys Eng Sci 454(1971):903-95, 1998), is arguably the most popular mathematical scheme for non-stationary signal decomposition and analysis. The objective of EMD is to separate a given signal into a number of components, called intrinsic mode functions (IMF’s) after which the instantaneous frequency (IF) and amplitude of each IMF are computed through Hilbert spectral analysis (HSA). On the other hand, the synchrosqueezed wavelet transform (SST), introduced by Daubechies and Maes (Wavelets in Medicine and Biology, pp. 527-46, 1996) and further developed by Daubechies et al. (Appl Comput Harmon Anal 30:243-61, 2011), is applied to estimate the IF’s of all signal components of the given signal, based on one single reference “IF function- under the assumption that the signal components satisfy certain strict properties of a so-called adaptive harmonic model, before the signal components of the model are recovered. The objective of our paper is to develop a hybrid EMD-SST computational scheme by applying a “modified SST-to each IMF of the EMD, as an alternative approach to the original EMD-HSA method. While our modified SST assures non-negative instantaneous frequencies of the IMF’s, application of the EMD scheme eliminates the dependence on a single reference IF value as well as the guessing work of the number of signal components in the original SST approach. Our modification of the SST consists of applying vanishing moment wavelets (introduced in a recent paper by C.K. Chui, Y.-T. Lin and H.-T. Wu) with stacked knots to process signals on bounded or half-infinite time intervals, and spline curve fitting with optimal smoothing parameter selection through generalized cross-validation. In addition, we formulate a local cubic spline interpolation scheme for real-time realization of the EMD sifting process that improves over the standard global cubic spline interpolation, both in quality and computational cost, particularly when applied to bounded and half-infinite time intervals.