Comparing Spectra of a Series of Point Events Particularly for Heart Rate Variability Data

Different methods for spectral analysis of the heart rate signal¿considered as series of point events¿are used in studies on heart rate variability. This paper compares these methods, focusing on the two principal ones: the interval spectrum, i.e., the spectrum of the interval series, and the spectrum of counts, which is related to the representation of the event series as a series of spikes (delta functions). Both autospectra are estimated for experimental heart rate data and are shown to produce similar results. This similarity is proven analytically, and it is shown that for small variations in interval length, the ratio of these spectra is PI(f)/PC(f) = [sin(¿f¿)/(¿f¿)]2, with PI and PC the interval spectrum and the spectrum of counts, respectively, f the frequency, and ¿the mean interval length. It is concluded that both autospectra are equivalent for the considered heart rate data, but that, when relating the heart rate signal to other signals (e.g., respiration, blood pressure) by means of cross spectra, the technique to be used depends on the characteristics of the second signal.