Spectral distortion properties of the integral pulse frequency modulation model

The integral pulse frequency modulation (IPFM) model has been used for the following two purposes. First, it has been utilized to verify the correspondence between the spectral structure of autonomic input and the estimated spectrum of heart rate variability (HRV), relying mainly on the theoretical work of Bayly (1968). Second, the IPFM model provides a framework for evaluating how precisely the proposed method of HRV analysis could estimate the input spectral structure. However, the appropriateness of the IPFM model for both purposes has not been examined sufficiently in realistic situations. In this paper, the spectral structure of the pulse train generated by the IPFM model is theoretically derived for an input signal containing multiple frequency components. This is a more general condition than the single sinusoidal input signal used earlier. In accordance with the theoretical results, the magnitude of the spectral distortion is computed for a pair of varied frequencies, considering the corresponding coefficient of variation of interpulse intervals. Results show that the distortion could be nonnegligible under practical values of the coefficient of variation. Such distortion may well affect the spectral structure in the wide frequency range. This study suggests that the spectral structure of HRV should be interpreted carefully, taking the above distortion properties into account, even though the IPFM model appears to be established as a mechanism mediating between autonomic input and heart rate variability.