Development of Decomposition Methods for Empirical Modes Based on Extremal Filtration

Abstract

The method of extremal filtration implementing the decomposition of signals into alternating components is considered. The history of the method development is described, its mathematical substantiation is given. The method suggests signal decomposition based on the removal of known components locally determined by their extrema. The similarity of the method with empirical modes decomposition in terms of the result is shown, and their comparison is also carried out. The algorithm of extremal filtration has a simple mathematical basis that does not require the calculation of transcendental functions, which provides it with higher performance with comparable results. The advantages and disadvantages of the extremal filtration method are analyzed, and the possibility of its application for solving various technical problems is shown, i.e. the formation of diagnostic features, rapid analysis of signals, spectral and time-frequency analysis, etc. The methods for calculating spectral characteristics are described: by the parameters of the distinguished components, based on the approximation on the extrema by bell-shaped pulses. The method distribution in case of wavelet transform of signals is described. The method allows obtaining rapid evaluation of the frequencies and amplitudes (powers) of the components, which can be used as diagnostic features in solving problems of recognition, diagnosis and monitoring. The possibility of using extremal filtration in real-time systems is shown.