Continuous representation of unevenly sampled signals - An application to the analysis of heart rate variability

Abstract

Various methods for the continuous representation of unevenly sampled physiological signals, especially of heart rate and heart rate variability have been published over the past two decades. Due to the mathematical difficulties of analyzing unevenly spaced event series or unevenly sampled signals, all of the previously described techniques are impeded by some severe limitations which result from either representing the signal based on an assumed and often insufficient physiological model of signal generation, or from simplifications in the selected signal processing tools. Though the described methods have their merits and allow sufficient description of heart rate in some special applications, there has been no systematic investigation into a continuous representation of unevenly sampled physiological signals which is free from any limitations or simplifying assumptions and which would allow an objective comparison of the known methods and the determination of the respective errors in order to decide which technique is the best suited for a specific application. In this paper a continuous representation of the point event series describing the temporal sequence of heart beats is presented which does not impose any limiting assumptions on the data analysis. The results obtained were validated through simulations in both time and frequency domains, and compared with the established techniques to allow the determination of errors at the specific times where the heart beats occur, as well as within the intervals between these sample points.