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A comparison of two Hilbert spectral analyses of heart rate variability

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Abstract

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.

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Notes

  1. See Chap. 6 in [24] and [21, 22] for further information of the application of stationary wavelet packet transformation in the present paper.

  2. In the present paper, the discrete Hilbert transform was used according to D(t) + iD H(t) = D(t) + i H D(t) where H denotes the Hilbert matrix implemented according to the hilbert.m algorithm in matlab.

  3. This step is necessary since M(t) is no longer a analytical vector by its zero coefficients for negative frequencies (see hilbert.m algorithm in matlab).

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Acknowledgment

I thank professor Sofia Olhede and professor Andrew T. Walden for providing me Matlab scripts for the HOW-transformation. Their help is highly appreciated. The Matlab emd.m script for the HH-transformation is available at http://www.ens-lyon.fr/~flandrin|/software.html [26].

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  1. Human Movement Science Programme, Norwegian University of Science and Technology, Dragvoll Idrettssenter, 7491, Trondheim, Norway

    Espen Alexander Fürst Ihlen

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  1. Espen Alexander Fürst Ihlen
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Correspondence to Espen Alexander Fürst Ihlen.

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Ihlen, E.A.F. A comparison of two Hilbert spectral analyses of heart rate variability. Med Biol Eng Comput 47, 1035–1044 (2009). https://doi.org/10.1007/s11517-009-0500-x

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