Distortion properties of the interval spectrum of IPFM generated heartbeats for heart rate variability analysis

The integral pulse frequency modulation (IPFM) model converts a continuous- time signal into a modulated series of ! vent times, often represented as a pulse train. The IPFM process is important to the field of heart rate vari ability (HRV) as a simple model of the sinus modulation of heart rate. In t his paper, we discuss the distortion properties associated with employing t he interval spectrum for the recovery of the input signal from an IPFM proc ess's output pulse train. The results state, in particular for HRV, how pre cisely the interval spectrum can be used to infer the modulation signal res ponsible for a series of heartbeats. We have developed a detailed analytica l approximation of the interval spectrum of an IPFM process with multiple s inusoids as the input signal. Employing this result, we describe the struct ure and the distortion of the interval spectrum. The distortion properties of the interval spectrum are investigated systematically for a pair of freq uency components. The effects of linear and nonlinear distortion of the fun damentals, the overall contribution of harmonic components to the total pow er, the relative contribution of "folded back" power due to aliasing and th e total distortion of the input spectrum are investigated. We also provide detailed comparisons between the interval spectrum and the spectrum of coun ts (SOC). The spectral distortion is significant enough that caution should be taken when interpreting the interval spectrum, especially for high freq uencies or large modulation amplitudes. Nevertheless, the distortion levels are not significantly larger than those of the SOC. Therefore, the spectru m of intervals may be considered a viable technique that suffers more disto rtion than the SOC.