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

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Abstract

Counting statistics in the form of the variance-time curve provides an alternative to spectral analysis for point processes exhibiting 1/f β-fluctuations, such as the heart beat. However, this is true only for β<1. Here, the case of general β is considered. To that end, the mathematical relation between the variance-time curve and power spectral density in the presence of 1/f β-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 β⩾1. Some applications to the analysis of heart rate variability are given.

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Authors and Affiliations

  1. Medizinische Universitätsklinik Würzburg, Josef-Schneider-Strasse 2, D-97080, Würzburg, Germany

    Rainer Scharf, Malte Meesmann & Jan Boese

  2. Santa Fe Institute, 1399 Hyde Park Road, 87501, Santa Fe, NM, USA

    Dante R. Chialvo

  3. Physiologisches Institut der Universität Würzburg, Röntgenring 9, D-97070, Würzburg, Germany

    Klaus -D. Kniffki

Authors
  1. Rainer Scharf
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  2. Malte Meesmann
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  3. Jan Boese
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  4. Dante R. Chialvo
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  5. Klaus -D. Kniffki
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Supported by the Wilhelm Sander-Stiftung, Munich

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Scharf, R., Meesmann, M., Boese, J. et al. General relation between variance-time curve and power spectral density for point processes exhibiting 1/f β-fluctuations, with special reference to heart rate variability. Biol. Cybern. 73, 255–263 (1995). https://doi.org/10.1007/BF00201427

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  • DOI: https://doi.org/10.1007/BF00201427

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