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EEG signal analysis by continuous wavelet transform techniques

M. Ende, P. Maaß , G. Mayer-Kress4(Finanziert mit Mitteln der DFG)

The basic goal of signal processing is to extract some desired information from a given set of measured data. Amongst the most powerful tools are time-frequency- or time-scale-representations of the signal. They can be obtained e.g. by Wigner-Ville-, Gabor- or wavelet transforms. Both types of representation aim at transforming and displaying the given data in such a way, that (in the case of a one-dimensional signal) a dominant value at , resp. at $(a,b)$, reflects the presence of a significant detail at time $t=b$ with local frequency $\omega$, resp. with size $a$.
The present investigation intends to highlight the power of wavelet transfroms for the detection of significant structures or unexpected events in EEG signals. The data under consideration was taken from an experiment, it consists of EEG measurements from various people which were exposed to different acoustic sequences. We will demonstrate the use of wavelet methods by analyzing the EEG measurement of five people which resulted from the sequence ``periodic, melody''.
Abbildung: EEG measurements, Fz electrodes, subjects c01104 and c01107
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A local extremum of $L_{\psi}f$ at $(a_0,b_0)$ therefore indicates a significant structure of size $a_0$ at time $b_0$. In the case of the Morlet-wavelet this can moreover be interpretate as the existence of a localized oscillation with frequency $\omega \ = \ 5/a_0$ at time $t=b_0$, hence in the following example, where EEG signals were sampled at a rate of 256 Hz, a local maximum at $a_0$ corresponds to a physical frequency of $\Omega = \omega / \tau$.
Abbildung: The indicator function $n(a)$ for subjects c01104 and c01107. Subject c01104 reacts strongly near $a \sim 15.5$, subject c01107 shows no reaction.
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Hence we display $L_{\psi}f$ with a fine discretization for $a \in (14,18]$, see Figure (3.8, left). According to

$\displaystyle L_{\psi}f(a,b)\ = \ \langle \ f \ , \ a^{-1/2}\psi\left( { \cdot - b \over a} \right)\ \rangle_{L^2(I\!\!R)}\
\ $     (3.1)

we search for local extrema which account for a localization in time of the significant reactions, Figure (3.8, right). Hence simple thresholding was performed on three electrodes (Fz, Cz, Pz) of person c01104.

Abbildung: The wavelet-transform of the Fz-measurement of subject c01104 zoomed to the intervall $a \in (14,18]$ (left), the most significant events after thresholding are marked in the $(b,a)$-plane (right). We erased a certain region around each detected event since a local extremum spreads over some area.
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next up previous contents
Nächste Seite: DFG Projekt: Das dynamische Aufwärts: Effiziente Wavelet-Algorithmen Vorherige Seite: BMFT-Projekt: Bilddatenkompression mit Wavelet-Methoden   Inhalt
Udo Schwarz 2006-09-18