TECHNOLOGIES FOR CALCULATING THE CORRELATION COEFFICIENT BETWEEN THE USEFUL SIGNAL AND THE NOISE USING THE ESTIMATE OF THEIR RELAY CROSS-CORRELATION FUNCTION

Abstract

It is shown that when noisy signals are formed, the condition for the absence of correlation between the useful signal and the noise is often violated. This causes certain errors of correlation analysis of these signals, resulting in the inadequacy of the results obtained. In addition, the existing correlation analysis technologies do not allow using the noise as a carrier of valuable information. Therefore, the full use of the colossal information potential of noisy signals requires new technologies that would exclude the loss of valuable information, both when the known classical conditions are met and when they are not. Algorithms are developed for determining the estimate of the correlation coefficient between the useful signal and the noise, which cannot be measured directly or isolated from a noisy signal. For this purpose, the normalized cross-correlation function between the useful signal and the noise is used. An algorithm for calculating the estimates of the normalized cross-correlation function between the useful signal and the noise is developed using the estimates of the relay correlation function of the noisy signal. It is shown that the value of this estimate, calculated at a zero time shift, is an estimate of the correlation coefficient between the useful signal and the noise. A technology for conducting computational experiments is proposed, a comparative analysis is carried out, and the reliability of the proposed algorithms and technologies is confirmed. It is shown that under the normal technical condition of the object, the estimates of the relay cross-correlation function and the correlation coefficient between the useful signal and the noise will be close to zero. With the emergence of various defects preceding malfunctions at the object, these estimates will change depending on the degree of damage. Therefore, it is the estimates of the cross-correlation function and the correlation coefficient between the useful signal and the noise that should be used in monitoring and control systems as informative attributes for signaling and monitoring the beginning of changes in the technical condition of objects and the dynamics of their malfunctions. The use of these new effective informative attributes makes it possible to increase the degree of accuracy and reliability of operation of modern information systems.