The Energy Spectrum of the Noise Modulation Function under the Influence of Slow Multiplicative Noise
V. M. Artyushenko, Vladimir Ivanovich Volovach · 2023
The effect of slow multiplicative noise on the energy spectrum of the noise modulation function is analyzed. Two cases of determining the energy spectrum are considered: with signal distortions described by a narrow-band normal stationary random process, and under the influence of pulse-fluctuation noise. The corresponding mathematical expressions of the energy spectra are obtained, including the case of deep phase distortions. It is shown that when narrow-band multiplicative noise affects the signal, a discrete component is present in the energy spectrum of the noise modulation function. Wherein the depth of the phase distortions will determine the power of said discrete component. The distribution pattern of the continuous part of the energy spectrum of phase distortion is determined by the ratio of the width of the named spectrum to its average frequency. With pulse-fluctuation modulating noise with a deterministic clock interval, the energy spectrum of the noise modulation function is the sum of continuous and discrete parts. Expressions are obtained for determining the discrete and continuous parts of the energy spectrum of the noise modulation function under the influence of modulation noise. The conditions under which the spectrum consists only of discrete components are given.