A comparison of two Hilbert spectral analyses of heart rate variability.

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.