Spectral contributions of sections of power-law structure function of random processes with stationary increments. Part 1. The exponent is less than one
V.A. Fedorov
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, 1, Academician Zuev square, Tomsk, 634055, Russia
Keywords: случайный процесс со стационарными приращениями, степенная структурная функция, спектральная плотность, спектральные вклады, random process with stationary increments, power-law structure function, spectral density, spectral contribution
Abstract
The frequency behavior of the spectral contributions of the initial, middle, and “finite” parts of the power-law structure function (with an exponent less than one) to the spectral density (SD) of a random process with stationary increments is considered. It is shown that it is considerably more complicated than the strictly positive monotonic power-law frequency dependence of the initial SD. The latter corresponds only to the behavior of the spectral contribution of the initial section of the given structure function. The analytical approximation dependences of the frequency behavior of all these spectral contributions are presented and analized. They are recommended for wide practical use.
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