A comparison of two Hilbert spectral analyses of heart rate variability

Original Article


The present paper compares the performance of two Hilbert spectral analyses when applied to a synthetic RR series from a nonstationary integral pulse frequency modulation model and to real RR series from a dataset of normal sinus arrhythmia. The Hilbert–Huang transformation based on empirical mode decomposition is compared to the presently introduced Hilbert–Olhede–Walden transformation based on stationary wavelet packet decomposition. The comparison gives consistent results pointing to a superior performance of the Hilbert–Olhede–Walden transformation showing 33–163 times smaller deviations when estimating the instantaneous frequency traces of the synthetic RR series. Artificial fluctuations caused by mode mixing in the Hilbert–Huang spectrum are seen in both the synthetic and real RR series. It can be concluded that the instantaneous frequencies and amplitudes estimated by the Hilbert–Huang transformation should be interpreted with caution when investigating heart rate variability.


Heart rate variability Hilbert–Huang spectrum Empirical mode decomposition Integral pulse frequency modulation Instantaneous frequency Wavelet transformation Time–frequency analysis 


  1. 1.
    Axelrod S, Gordon D, Ubel FA, Shannon DC, Barger AC, Cohen RJ (1981) Power spectrum analysis of heart rate fluctuation: a quantitative probe of beat to beat cardiovascular control. Science 213:220–222CrossRefGoogle Scholar
  2. 2.
    Balocchi R, Meniccuci D (2004) Deriving the respiratory sinus arrhythmia from the heartbeat time series using empirical mode decomposition. Chaos Solitons Fractals 20:171–177MATHCrossRefGoogle Scholar
  3. 3.
    Bayly E (1968) Spectral analysis of the pulse frequency model in the nervous system. IEEE Trans Bio Med Eng 4:257–365CrossRefGoogle Scholar
  4. 4.
    Bernardi L, Leuzzi S, Radaelli A, Passino C, Johnston JA, Sleight P (1994) Low-frequency spontaneous fluctuations of R–R interval and blood pressure in conscious humans: a baroreceptor or central phenomenon? Clin Sci 87:649–654Google Scholar
  5. 5.
    Berger R, Akselrod S, Gordon D, Cohen R (1986) An efficient algorithm for spectral analysis of heart rate variability. IEEE Trans Biomed Eng 33:900–904CrossRefGoogle Scholar
  6. 6.
    Boashash B (1992) Estimating and interpreting the instantaneous frequency of a signal-part 2: algorithms and applications. Proc IEEE 80:540–568CrossRefGoogle Scholar
  7. 7.
    Cevese A, Gulli G, Polati E, Gottin L, Grasso R (2001) Baroreflex and oscillations of heart period at 0.1 Hz studied by alpha-blockade and cross-spectral analysis in healthy humans. J Physiol 531:235–244CrossRefGoogle Scholar
  8. 8.
    De Boer R, Karemaker J, Strackee J (1985) Spectrum of a series of point events, generated by the integral pulse frequency modulation model. Med Biol Eng Comput 23:138–142CrossRefGoogle Scholar
  9. 9.
    Deering R, Kaiser JF (2005) The use of a masking signal to improve empirical mode decomposition. In Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), pp 485–488Google Scholar
  10. 10.
    Echeverria JC, Crowe JA, Woolfson MS, Hayes-Gill BR (2001) Application of empirical mode decomposition to heart rate variability analysis. Med Biol Eng Comput 39:471–479CrossRefGoogle Scholar
  11. 11.
    Eckberg DL (1997) Sympathovagal balance. A critical appraisal. Circulation 96:3226–3232Google Scholar
  12. 12.
    Goldberger A, Amaral L, Glass L, Hausdorff J, Ivanov P, Mark R, Mietus J, Moody G, Peng C, Stanley E (2000) PhysioBank, PhysioToolkit, and PhysioNet. Components of a new research resource for complex physiological signals. Circulation 101:e215–e220Google Scholar
  13. 13.
    Hayano J, Taylor JA, Mukai S, Okada A, Watanabe Y, Takata K, Fujinami T (1994) Assessment of frequency shifts in R–R interval variability and respiration with complex demodulation. J Appl Physiol 77(6):2879–2888Google Scholar
  14. 14.
    Holland A, Aboy M. (2009) A novel recursive Fourier transform for nonuniform sampled signals: application to heart rate variability spectrum estimation. Med Biol Eng Comput (in press)Google Scholar
  15. 15.
    Huang NE, Shen Z, Long S, Wu M, Shih H, Zheng Q, Yen N, Tung C, Liu H (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc A 454:903–995MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Huang NE, Wu M-LC, Long SR, Shen SSP, Qu W, Gloersen P, Fan KL (2003) A confidence limit for the empirical mode decomposition and Hilbert spectral analysis. Proc R Soc A 459:2317–2345MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Maestri R, Pinna GD, Accardo A, Allegrini P, Balocchi R, D’addio G, Ferrario M, Menicucci D, Porta A, Sassi R, Signorini MG, La Rovere MT, Cerutti S (2007) Nonlinear indices of heart rate variability in chronic heart failure patients: redundancy and comparative clinical value. J Cardiovasc Electrophysiol 18(4):425–433CrossRefGoogle Scholar
  18. 18.
    Malliani A, Pagani M, Montano N, Mela S (1998) Sympathovagal balance: a reappraisal. Circulation 98:2640–2642Google Scholar
  19. 19.
    Nakao M, Norimatsu M, Mizutani Y, Yamamoto M (1997) Spectral distortions properties of the Integral Pulse Frequency Modulation Model. IEEE Trans Biomed Eng 44:419–426CrossRefGoogle Scholar
  20. 20.
    Neto EPS, Custaud MA, Cejka JC, Abry P, Frutoso J, Gharib C, Flandrin P (2004) Assessment of cardiovascular autonomic control by the empirical mode decomposition. Meth Inform Med 1:60–65Google Scholar
  21. 21.
    Neto EPS, Abry P, Loiseau P, Cejka JC, Custaud MA, Frutoso J, Gharib C, Flandrin P (2007) Empirical mode decomposition to assess cardiovascular autonomic control in rats. Fundam Clin Pharmacol 21(5):481–496CrossRefGoogle Scholar
  22. 22.
    Nielsen M (2001) On the construction and frequency localization of finite orthogonal quadrature filters. J Approx Theory 108:36–52MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Olhede S, Walden AT (2004) The Hilbert spectrum via wavelet projections. Proc R Soc A 460:955–975MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Olhede S, Walden AT (2005) A generalized demodulation approach to time-frequency projections for multicomponent signal. Proc R Soc A 461:2159–2179MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Percival DB, Walden AT (2000) Wavelet methods for time series analysis. Cambridge University Press, Cambridge, pp 206–253MATHGoogle Scholar
  26. 26.
    Ponomarenko VI, Prokhorov MD, Bespyatov AB, Bodrov MB, Gridnev VI (2005) Deriving main rhythms of the human cardiovascular system from the heartbeat time series and detecting their synchronization. Chaos Solitons Fractals 23:1429–1438MATHGoogle Scholar
  27. 27.
    Rajendra Acharya U, Paul Joseph K, Kannathal N, Lim CM, Suri JS (2006) Heart rate variability: a review. Med Biol Eng Comput 44(12):1031–1051CrossRefGoogle Scholar
  28. 28.
    Rilling G, Flandrin P, Goncalves P (2003) On empirical mode decompositions and its algorithms. IEEE-EURASIP NSIP, Grado, ItalyGoogle Scholar
  29. 29.
    Sörnmo L, Laguna P (2005) Bioelectrical signal processing in cardiac and neurological application. Elsevier Academic Press, London, pp 567–621CrossRefGoogle Scholar
  30. 30.
    Sleight P, Bernardi P (1998) Sympathovagal balance. Circulation 98:2640Google Scholar
  31. 31.
    Stein P, Kleiger E (1999) Insights from the study of the heart rate variability. Ann Rev Med 50:249–261CrossRefGoogle Scholar
  32. 32.
    Task Force European Society of Cardiology and North American Society of Pacing Electrophysiology (1996) Heart rate variability. Standards of measurement, physiological interpretation, and clinical use. Eur Heart J 17:354–381Google Scholar
  33. 33.
    Zhong Y, Bai Y, Yang B, Ju K, Shin KS, Lee MH, Jan K-M, Chon KH (2007) Autonomic nervous nonlinear interactions lead to frequency modulation between low- and high-frequency bands of the heart rate variability spectrum. Am J Physiol Integr Comp Physiol 293:R1961–R1968Google Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2009

Authors and Affiliations

  1. 1.Human Movement Science ProgrammeNorwegian University of Science and TechnologyTrondheimNorway

Personalised recommendations