Abstract. The frequency properties of a signal modulated by a random process with a nonzero average frequency are investigated. It is shown that the energy spectrum of frequency-modulated harmonic oscillation is infinitely wide and contains a discrete spectral line and a partial region at the frequency of the modulated oscillation, as well as partial regions corresponding to the harmonics of the middle frequency of the modulating narrow-band random signal relative to the modulated oscillation frequency. The spectral regions width depends on the variance and number of the corresponding harmonic of the average frequency of the modulating signal. Results of calculations of the energy spectrum of frequency-modulated harmonic oscillations are presented. It is noted that derived relations for the correlation function and the energy spectrum of the frequency-modulated signal can be used in study and development of information transmission systems with angular modulation of the carrier wave.

Keywords: frequency modulation, random signal, correlation function, energy spectrum

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