General relation between variance-time curve and power spectral density for point processes exhibiting 1/f beta-fluctuations, with special reference to heart rate variability.

Counting statistics in the form of the variance-time curve provides an alternative to spectral analysis for point processes exhibiting 1/f beta-fluctuations, such as the heart beat. However, this is true only for beta < 1. Here, the case of general beta is considered. To that end, the mathematical relation between the variance-time curve and power spectral density in the presence of 1/f beta-noise is worked out in detail. A modified version of the variance-time curve is presented, which allows us to deal also with the case beta > or = 1. Some applications to the analysis of heart rate variability are given.