Correlation Functions of the Noise Modulation Function under the Influence of Stationary and Slow Multiplicative Noise

An approach for determining the correlation functions of the noise modulation function under the influence of modulating (or more often multiplicative) noise is described. Both stationary and slow noise is considered as influencing multiplicative noise. Correlation functions of noise modulation and fluctuations of the latter can be found by the four-dimensional characteristic function of phase and amplitude distortions. We have derived expressions for the abovementioned correlation functions affected by static multiplicative noise for the normal law of variation of amplitude and phase distortions in the case of their uncorrelation and cross-correlation. The correlation functions of noise modulation and noise modulation function fluctuations under the influence of slow modulating noise were determined for the case when the phase and distortion amplitude variations are independent. The expressions of the correlation functions of noise modulation and its fluctuations for correlated and normal distribution of phase and amplitude distortions under the influence of slow modulating noise are obtained.