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In-Depth Information
3.1 Introduction
Electroencephalographic (EEG) measures have been successfully used in the past as
indices of cerebral engagement in cognitive tasks or in the identification of certain
brain pathologies. Higher brain functions typically require the integrated, coordi-
nated activity of multiple specialized neural systems that generate EEG signals at
various brain regions. Linear [7,18] and nonlinear signal analysis methods have been
applied in order to derive information regarding patterns of local and coordinated
activity during performance of specific tasks [11] or in various pathologies [2, 13].
The inherent complexity and the dynamic nature of brain function make the eval-
uation using EEG a rigorous job. Nevertheless, EEG signal analysis provides the
advantage of high time resolution and thus it can deduce information related to both
local and widespread neuronal activations in short-time periods, as well as their time
evolution.
Traditional spectral analysis techniques with Fourier transform (FT) and more
specifically the windowed power spectral density function, known as the peri-
odogram [16], form the most commonly used analytical tool for spectral represen-
tation and evaluation of activity on different EEG frequency bands [7, 15] - namely
delta (
)
. However, this approach
considers the EEG signal as a stationary process, which assumption is not satisfied in
practice, thus restricting the actual confidence on results. A more promising method-
ology is based on the time-varying spectral analysis that takes into account the
nonstationary dynamics of the neuronal processes [1]. The short-time Fourier
(STFT) and the wavelet transforms are the most prevalent analysis frameworks of
this class. The first approach uses a sliding time window, whereas the second one
forms the projection of the signal onto several oscillatory kernel-based wavelets
matching different frequency bands. Currently, such time-varying methods have
been widely applied in event-related potential (ERP) data, where distinct waveforms
are associated with an event related to some brain function [3]. Under certain as-
sumptions, both time-frequency transforms are in fact mathematically equivalent,
since they both use windows that under certain conditions can provide the same
results [4]. The reason why these approaches are often regarded as different lies
in the way they are used and implemented. Wavelet transform (WT) is typically
applied with the relative bandwidth (
δ
), theta (
θ
), alpha (
α
), beta (
β
), and gamma (
γ
f
) held constant, whereas the Fourier ap-
proach preserves the absolute bandwidth (
Δ
f
/
f
) constant. In other words, STFT uses
an unchanged window length, which leads to the dilemma of resolution; a narrow
window leads to poor frequency resolution, whereas a wide window leads to poor
time resolution. Consequently, according to the Heisenberg uncertainty principle
one cannot accurately discriminate frequencies in small time intervals. However,
the WT can overcome the resolution problem by providing multiresolution analy-
sis. The signal may be analyzed at different frequencies with different resolutions
achieving good time resolution but poor frequency resolution at high frequencies
and good frequency resolution but poor time resolution at low frequencies. Such
a setting is suitable for short duration of higher frequency and longer duration of
lower frequency components of the EEG bands. For the purposes of this study the
wavelet approach is used.
Δ
