Application of a New Method of Spectral Analysis for Detecting Synchronous Processes in Heliobiology
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Until now, the sum of periodic variations was the main carrier of information in biological and heliogeophysical signals. However, not all of the time series of interest contain dominant periodic components. The relaxation analysis used in this paper makes it possible to generalize the “spectral” formalism to signals that cannot be represented as a sum of a limited number of quasiperiodic components. An algorithm for filtering noise and long-period trends is developed based on the separation of the original signal into rapidly and slowly relaxing components. The main theorem that guarantees the operability of the algorithm is proven. A method for constructing an orthonormal basis whose components have a strictly defined relaxation time is described. The result of the signal expansion over this basis is called the relaxation spectrum. It can be used to divide the time series into signal-to-noise or oscillation-trend if there are no adequate Fourier or stochastic models. The hypothesis that geomagnetic rhythms with periods of about 7 and 9 days have the most significant influence on physiological indicators of biological objects (including those of the population as a whole), as was stated earlier by the heliobiologists, is confirmed based on an automatic algorithm for extracting reliable spectral peaks of population and heliogeomagnetic time series and detecting similar peaks using the Sørensen measure.
Keywords:spectral formalism generalization signal filtering orthonormal basis generation heliobiophysics
This work was supported by the Russian Foundation for Basic Research, project no. 15-04-02945.
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