Algorithms for determining the coefficient of correlation and cross-correlation function between a useful signal and noi
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NEW MEANS OF CYBERNETICS, INFORMATICS, COMPUTER ENGINEERING, AND SYSTEM ANALYSIS ALGORITHMS FOR DETERMINING THE COEFFICIENT OF CORRELATION AND CROSS-CORRELATION FUNCTION BETWEEN A USEFUL SIGNAL AND NOISE OF NOISY TECHNOLOGICAL PARAMETERS T. A. Aliev,a† G. A. Guliyev,a‡ F. H. Pashayev,a†† and A. B. Sadiqova†‡
UDC 519.216
Abstract. This paper considers various possible variants of determining estimates of cross-correlation functions and coefficients of correlation between a useful signal and noise. Their advantages and drawbacks are analyzed. For practical applications, easily implemented technologies are proposed for approximately determining estimates of the cross-correlation function and coefficient of correlation between a useful signal and noise of technological parameters obtained from outputs of definite sensors during the operation of objects. Algorithms are given that indicate the moment of emergence of a distinction of the mentioned estimates from zero. Keywords: noise, noisy signal, crosscorrelation function, correlation coefficient, defect. INTRODUCTION It is well known [1–8] that, in solving numerous applied monitoring and control problems with the use of traditional technologies of random signal analysis, acceptable results can be obtained only when the conditions of stationarity, normality of the distribution law, absence of correlation between noise and a useful signal, etc. are fulfilled. However, for many real-life technological parameters obtained from sensor outputs, these conditions are not fulfilled. Therefore, the adequacy of the description of many processes analyzed with the help of probabilistic-statistical methods turns out to be unsatisfactory and, within the framework of classical theories of analysis of random processes, many problems of tremendous economic and social significance are rather frequently not solved. This leads to insufficient realization of vast capabilities inherent in technologies of analysis of random processes. For example, the elimination of drawbacks of the traditional technology would allow one to increase the reliability and efficiency of forecasting earthquakes and all other possible natural disasters, disease diagnosis, exploration activity, prediction of failures of thermal and atomic power stations and failures in drilling oil wells, preflight diagnostics of the technical state of airplanes, creations of adequate mathematical models, etc. In this connection, to obtain reliable results for numerous applied problems, along with the use of the potential of traditional technologies, new alternative algorithms should be created that would provide the accuracy of obtained estimates under both fulfilled and unfulfilled corresponding classical conditions.
a
Institute of Cybernetics, Azerbaijan Academy of Sciences, Baku, Azerbaijan, †[email protected]; [email protected]; ††[email protected]; †‡[email protected]. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 169–178, May–June 2011. Original article submitted January 29, 2010.
‡
1060-0396/11/4703-0481
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