Operators of fractional integration and their applications
Applied Mathematics and Computation
Time domain design of fractional differintegrators using least-squares
Signal Processing - Fractional calculus applications in signals and systems
Computer Methods and Programs in Biomedicine
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Fractional differintegration is used as a new tool to characterize heart rate variability time series. This paper proposes and focuses in two indexes (@a"c and fnQ) derived from the fractional differintegration operator. Both indexes are applied to fractional Gaussian noise (fGn) and actual RR time series in order to test their behavior. In the analysis of monofractal time series, @a"c is linearly related with the Hurst exponent and the estimation of the exponent by the proposed index has lower variance than by using Detrended Fluctuation Analysis (DFA) or the periodogram. The other index fnQ quantifies how the time series adjust to a monofractal time series. Age, postural changes and paced breathing cause significant changes on fnQ while @a"c only shows significant changes due to posture. In the analyzed actual HRV time series, @a"c shows good correlation with the short term scaling exponent obtained by DFA, LF/HF and RMSSD while no correlations have been found for fnQ.