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Heart rate time series

Here we have two interesting time series, series 1 (13K text), and series 2 (13K text). We invite you to download these time series to explore their properties. (If you are using Netscape, this can be done most easily by pressing and holding the Shift key while clicking on the links above -- this will open a dialog box that allows you to specify the name and location of the downloaded file on your computer.)

Each series contains 1800 evenly-spaced measurements of instantaneous heart rate from a single subject. The two subjects were engaged in comparable activities for the duration of each series. The measurements (in units of beats per minute) occur at 0.5 second intervals, so that the length of each series is exactly 15 minutes. As can be easily confirmed, the means and standard deviations of the heart rate measurements are nearly identical in the two subjects. Are these series therefore equivalent in terms of heart rate variability (HRV)?

We suggest that you begin your exploration of these series by plotting them. (You may view low-resolution plots of series 1 and series 2 here.) Visual inspection will reveal marked differences that are not reflected in moment statistics such as mean and standard deviation. How can these differences be characterized?

One way to do so is to study the frequency content of these time series. Examine the power spectrum of series 1, and the power spectrum of series 2. The rapid oscillations visible in series 1 are reflected in its power spectrum by a peak near 0.1 Hz (most likely, the frequency of respiration in this subject); thus this component of HRV is probably respiratory sinus arrhythmia, a modulation of heart rate that is greatest in young subjects, and gradually decreases in amplitude with increasing age. By contrast, almost all of the power in series 2 is concentrated at a much lower frequency (about 0.02 Hz). These dynamics are commonly observed in the context of congestive heart failure, where circulatory delays interfere with regulation of carbon dioxide and oxygen in the blood, leading to slow oscillations of heart rate.

Calculations of the heart rates from the original (non-uniform) series of beat occurrence times were performed using the IPFM method as implemented by tach. If you wish to experiment with other heart rate time series, find out how to use tach and related software in PhysioNet's RR Intervals, Heart Rate, and HRV Howto.

If you found this comparison interesting, consider series 3 (7K text) and series 4 (7K text). These heart rate time series contain data derived in the same way as for the first two, although these two series contain only 950 measurements each, corresponding to 7 minutes and 55 seconds of data in each case. As for the first pair, the means and standard deviations are similar. (You may view low-resolution plots of series 3 and series 4 here.) You will find that the power spectra (view the series 3 spectrum, and the series 4 spectrum) of these two time series are also quite similar, even though their dynamics differ significantly. Observations such as these suggest that neither first-order statistics nor frequency-domain analyses of HR time series reveal all of the information hidden in heart rate variations.


Goldberger AL, Rigney DR. Nonlinear dynamics at the bedside. In: Glass L, Hunter P, McCulloch A, eds. Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function. New York: Springer-Verlag, 1991, pp. 583-605.

George B. Moody (
Ary L. Goldberger, M.D. (
17 October 1996 (links updated 14 July 2005)

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