Pole-tracking algorithms for the extraction of time-variant heart rate variability spectral parameters

Abstract
Various algorithms of autoregressive (AR) recursive identification make it possible to evaluate power spectral distribution in correspondence with each sample of a time series, and time-variant spectral parameters can be calculated through the evaluation of the pole positions in the complex z-plane. In traditional analysis, the poles are obtained by zeroing the denominator of the model transfer function, expressed as a function of the AR coefficients. In this paper, two algorithms for the direct updating and tracking of movements of poles of an AR time-variant model on the basis of the innovation given to the coefficients are presented and investigated. The introduced algorithms are based upon 1) the classical linearization method and 2) a recursive method to compute the roots of a polynomial, respectively. In the present paper, applications in the field of heart rate variability (HRV) signal analysis are presented and efficient tools are proposed for quantitative extraction of spectral parameters (power and frequency of the low-frequency (LF) and high-frequency (HF) components) for the monitoring of the action of the autonomic nervous system in transient patho-physiological events. These computational methods seem to be very attractive for HRV applications, as they inherit the peculiarity of recursive time-variant identification, and provide a more immediate comprehension of the spectral process characteristics when expressed in terms of poles and AR spectral components.