CROSS-CORRELATION OF A MULTIDIMENSIONAL SYSTEM
DOI:
https://doi.org/10.26906/SUNZ.2021.4.016Keywords:
correlation analysis, multidimensional linear system, even and odd components, continuity, random variablesAbstract
The subject of research in the article is the peculiar behavior of the mutual correlation functions of generalized coordinates - the presence of a discontinuity of the first kind when the argument passes from its positive values to negative ones. The goal is to assess the possibility of forming a gap between the even and odd components of the correlation function and to substantiate this phenomenon. Applied methods: comparison of two functions of real variables based on the Fourier transform, statistical methods of data analysis, theory of random functions, correlation analysis. The obtained results: construction of principles for obtaining even and odd components of the correlation function of a multidimensional linear system with an analysis of their continuity in the general sense; the interpretation of such expressions is proposed as the limit of a sequence of continuous functions, which ensures their continuity in the general sense and eliminates the inconsistency that has arisen in this case. The practical significance of the work lies in the construction of a model of cross-correlation of generalized coordinates of a linear system, taking into account the peculiarities of the behavior of the correlation functions.Downloads
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