Technologies for Analyzing and Calculating the Relationship between the Useful Component and the Noise of Noisy Signal in Monitoring Systems

The article is devoted to the development of algorithms for calculating the cross-correlation function and the correlation coefficient between the useful signal and the noise of a noisy signal. The authors analyze the factors influencing the adequacy of the results of solving the problems of monitoring, control, management, etc. It is noted that when processing noisy signals, algorithms and technologies for separate processing of the useful component and the noise should be used. It is shown that in the event of malfunctions, such an important condition as the absence of correlation between the useful signal and the noise is violated in monitoring and control systems. Therefore, the problem arises of calculating the crosscorrelation function and the correlation coefficient between the useful signal and the total noise as well. Algorithms are proposed for calculating the estimates of the correlation coefficient and the correlation function between the useful signal and the noise of noisy signals. It is pointed out that the moment of occurrence of the correlation between the useful signal and the noise can be monitored in real time in information systems. It is shown that the estimate of the variance of the total noise before the appearance of the correlation is a stable value. When a correlation appears, the value of the variance of the total noise changes. The difference in the variance estimates is taken as an analogue of the estimate of the cross-correlation function between the useful signal and the noise at zero time shift.A technology for conducting computational experiments is proposed. Discrete values of the useful signal, noise and noisy signal are generated. The correlation coefficient and the cross-correlation function between the useful signal and the noise are calculated by the developed and traditional algorithms. A comparative analysis is carried out. It is shown that the proposed technologies for calculating the estimates of the cross-correlation function and the correlation coefficient between the useful signal and the noise, as well as the variance of the total noise, make it possible to extract additional important information from noisy signals. This opens up the opportunity to increase the efficiency of the analysis of noisy signals.