Wavelet packet decomposition EEG on the basic frequency rhythms

This work is devoted to the study of signal electroencephalogram (EEG) by wavelet analysis methods. Traditionally for study of EEG, statistical methods and methods of the analysis Fourier are used. It is considered that the upper boundary frequency of normal EEG, noticeably influencing on its form does not exceed 30 Hz. The fact that higher frequencies are not visible, and in the Fourier spectrum of all EEG signal, the power spectrum of low-frequency part of EEG signal far exceeds and overrides the power spectrum of high frequency oscillations therefore the high frequency ranges are also practically closed for study. Wavelet analysis allows decomposing the entire EEG signal into separate components, which include both traditional rhythms: Delta, Theta, Alpha, Beta and Gamma and series of new frequency localized rhythms. This allows to consider them independently of each other and makes it possible to study separately the frequency and other properties of each component, including high frequency which poorly known at present. In this paper, we propose a new approach for obtaining numerical characteristics of the EEG based on the multilevel wavelet package decomposition and applying the Hilbert transformation, which allows to clearly allocate new frequency bands, to obtain visualization, and new numerical characteristics of the EEG. It is shown that by the wavelet decomposition up to the 6th level with the Meyer wavelet, the EEG signal is decomposed into wavelet components EEG = RecD₁ + RecD₂ + RecD₃ + RecD₄ + RecD₅ + RecD₆ + RecA₆, where RecD₄, RecD₅, RecD₆, and RecA₆ are classic ranges of Beta, Alpha, Theta and Delta, respectively, and the other RecD₁, RecD₂ , and RecD3 represent the part of the signal, which is usually called Gamma range. In this case, the range RecD1 has a relative l-energy of about 10, and its frequency spectrum is allocated from 75 to 250 Hz, therefore RecD₁ not considered in this work as a separate range of EEG signal. Frequency spectra of the components RecD₂ and RecD₃ are localized: RecD₃ - from 28 Hz to 50 Hz and RecD₂ - from 57 Hz to 75 Hz. In the work these ranges are named Gamma-2 and Gamma-1, respectively. In addition to the common numeric characteristics of all the bands, in this work three characteristics are defined: the relative energy of component, the average instantaneous frequency and the average statistical frequency of component. The calculation of these parameters for 256 fragments of EEG signal are conducted (in 4 fragments with a duration of 8 seconds, for each of the 64 channels of EEG) for the patient as open as with eyes closed. Calculations show that these numerical characteristics differ significantly for different EEG channels, this suggests that these parameters record the electrical activity of different brain regions. It is also shown that they depend on the recording conditions of EEG (with open or closed eyes). It turned out that the average instantaneous and average statistical frequency for the high-frequency components RecD2 and RecD3 behave unstably in case of small shifts of the fragment of the signal. The reason is that a significant part of their frequency spectra of power although is localized, but is distributed widely: from 28 Hz to 50 Hz or from 57 Hz to 75 Hz, respectively. These EEG components need further decomposition into narrower frequency ranges. For better frequency localization, these components are decomposed into several parts using the wavelet packet decomposition. In each case, the packet nodes of the tree decomposition are found, which allow to decompose RecD2 and RecD3 on new bands with good frequency localization: RecD₃ = RecD₃,(6, 10) + RecD_3X6, 12) + RecD_3X6, 13) + RecD_3X6, 14) + RecD_3X6, 15), RecD₂ = RecD₂ (5 13) + RecD₂,_a, 48) + RecD_w, 49) + RecD_w, 50) + RecD_w, 51) . The relative energy and average frequencies are calculated for obtained ranges. Thus, in this work, additionally to four classical EEG rhythms 10 bands with good frequency localization are found, which allow to determine their frequency characteristics.

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