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Title: Классификация процессов в инфокоммуникационных радиотехнических системах с применением BDS-статистики
Authors: Васюта, К. С.
Keywords: форма сигнала
классификация сигналов
BDS – статистика
Issue Date: 2012
Publisher: Проблеми телекомунікацій
Citation: Васюта К. С. "Классификация процессов в инфокоммуникационных радиотехнических системах с применением BDS-статистики." Проблеми телекомунікацій. – 2012. – № 4 (9). – С. 63 - 71.
Abstract: The paper formalizes the concept of "form" of the signal (the process) and is more seen as an informative sign than its energy. Differences in the "filling" of the phase space by attractors of different classes of processes and, as a consequence, in the dependence of the dimension correlation on the dimension of the embedding points to the one of the ways to classify observations. Manifestation of attractor structure indicates a relationship of elements in the observed process. In this interpretation, classes of processes (random, chaotic, regular) can be "metrized" (scaled). If necessary, further division of classes into subclasses (e.g., linear and nonlinear, stationary and nonstationary) may be mentioned. These classes and their separations will have a different "form" which is conveniently characterized by the amount of the dimension correlations. Formalization is made by the following chain of transformations: the "form" of the process ? dependence of values of the process ? structured attractor process ? criterion of dependence (dynamic or statistical) ? measure of dependence (e.g. dynamic invariants: Lyapunov exponents, dimension correlation or entropy). This interpretation of the term "waveform" allows to implement a scale to describe from the equal positions random, chaotic and deterministic processes. The classification of these processes is carried out with the use of BDS-statistics that identifies processes with a given probability under low signal noise ratio. Evaluation limits of applicability of this method for classification of processes showed that the values of BDS-statistics allow to detect ("metrize") regular and chaotic processes with high probability under low signal-to-noise ratio (q=3). In addition it can distinguish transformed linear and nonlinear stochastic processes and multifractal L?vy processes with probability more than 0,6 at (q=3), and classify with probability 1. The effectiveness of this method is explained by the fact that in contrast to the traditional methods for analysis of observations, BDS-statistics provides information about the structure of the process, which is stored in the values of the dimension correlation, its image in pseudophase embedding space, i.e. use of the additional information about properties of a signal.
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