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Atmospheric and Oceanic Optics

2021 year, number 11

Spectral contributions from sections of the power-law structure function of stationary random processes

V.A. Fedorov
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Keywords: stationary random process, power-law structure function, spectral density, spectral contribution


The frequency behavior of spectral contributions from initial, central, and “final” sections of the power-law structure function to the spectral density of a stationary random process is considered. Their oscillating alternating-sign frequency character is demonstrated. As the frequency increases, the rate of decrease in the absolute values of these contributions approaches the inversely proportional dependence. Simple analytical approximated relationships describing the frequency behavior of the spectral contributions are suggested and analyzed. They are recommended for wide practical use. The application of the obtained relationships for more complex composite power-law functions is considered.