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Extraction of Components from the TFR

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Nonlinear Mode Decomposition

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

This chapter considers extraction of components and estimation of their parameters based on the WFT and WT, discussing the methods that can be used for these tasks and related issues.

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References

  1. A.K. Barros, N. Ohnishi, Heart instantaneous frequency (HIF): an alternative approach to extract heart rate variability. IEEE Trans. Biomed. Eng. 48(8), 850–855 (2001)

    Article  Google Scholar 

  2. R. Bellman, Dynamic Programming (Princeton University Press, Princeton NJ, 1957)

    MATH  Google Scholar 

  3. D.P. Bertsekas, Dynamic Programming and Optimal Control (Athena Scientific, Belmont, 1995)

    MATH  Google Scholar 

  4. R.A. Carmona, W.L. Hwang, B. Torresani, Characterization of signals by the ridges of their wavelet transforms. IEEE Trans. Sig. Proc. 45(10), 2586–2590 (1997)

    Article  Google Scholar 

  5. R.A. Carmona, W.L. Hwang, B. Torresani, Multiridge detection and time-frequency reconstruction. IEEE Trans. Sig. Proc. 47(2), 480–492 (1999)

    Article  Google Scholar 

  6. I. Daubechies, J. Lu, H. Wu, Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool. Appl. Comput. Harmon. Anal. 30(2), 243–261 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  7. N. Delprat, B. Escudie, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torrésani, Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies. IEEE Trans. Inf. Theor. 38(2), 644–664 (1992)

    Article  MATH  Google Scholar 

  8. D. Iatsenko, A. Bernjak, T. Stankovski, Y. Shiogai, P.J. Owen-Lynch, P.B.M. Clarkson, P.V.E. McClintock, A. Stefanovska, Evolution of cardio-respiratory interactions with age. Phil. Trans. R. Soc. Lond. A 371(1997), 20110622 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  9. D. Iatsenko, P.V.E. McClintock, A. Stefanovska, On the extraction of instantaneous frequencies from ridges in time-frequency representations of signals. (2014), http://arxiv.org/abs/1310.7276

  10. D. Iatsenko, P.V.E. McClintock, A. Stefanovska, Linear and synchrosqueezed time-frequency representations revisited: overview, standards of use, reconstruction, resolution, concentration, and algorithms. Dig. Sig. Proc. (2015). doi:10.1016/j.dsp.2015.03.004 (in press)

  11. J.M. Lilly, S.C. Olhede, On the analytic wavelet transform. IEEE Trans. Inf. Theor. 56(8), 4135–4156 (2010)

    Article  MathSciNet  Google Scholar 

  12. M.B. Lotric, A. Stefanovska, D. Stajer, V. Urbancic-Rovan, Spectral components of heart rate variability determined by wavelet analysis. Physiol. Meas. 21(4), 441 (2000)

    Article  Google Scholar 

  13. S. Mallat, A Wavelet Tour of Signal Processing, 3rd edn. (Academic Press, Burlington, 2008)

    Google Scholar 

  14. G. Thakur, E. Brevdo, N.S. Fuckar, H.-T. Wu, The synchrosqueezing algorithm for time-varying spectral analysis: robustness properties and new paleoclimate applications. Sig. Process. 93(5), 1079–1094 (2013)

    Article  Google Scholar 

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Correspondence to Dmytro Iatsenko .

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Iatsenko, D. (2015). Extraction of Components from the TFR. In: Nonlinear Mode Decomposition. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-20016-3_3

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