Quantitative analysis of EEG signals: Time-frequency methods and ...

correlated with the denition of the P300 response. There are no decreases of entropy
correlated with the P100 response. This is consistent with the distribution of energy
described in g. 32, since the P100 peaks have a wide-band frequency composition
corresponding to alpha and theta oscillations. On the other hand, the P300 response
corresponded only to delta oscillations, thus having a lower entropy. It is very interesting
to note that the results of the entropy are not directly related with the ones of the energy.
This can be clearly seen, for example, by analyzing the TARGET response of electrode
O1, where there is a high energy increase at about 200ms without signicant changes in
the entropy for this time.
Considering the whole group of subjects, the grand average of the WS is shown in
gure 34. As pointed out with the typical subject, posterior decreases are observable
upon TARGET stimulation at about 600 ms, these decreases being clearly correlated
with the denition of the P300 response. On the contrary, P100 peaks produced no
relevant decreases in the entropy since they corresponded to a wider range of frequencies.
In order to verify statistically the decreases of entropy correlated with the P300
responses, pre- and post-stimulus mean entropy values were compared by using t-tests.
As shown in gure 35, entropies are signicantly decreased in posterior electrodes upon
TARGET stimulation. Then, entropy decreases respond to a dynamical process related
with the stimulation, rather than to random uctuations.
6.3.3 Discussion
Results of the calculation of the WS in dierent digitally generated signals conrmed
the expected correlation between the WS and the complexity of them, being high for
the random signal and low for the sinusoidal one. This shows that WS could be used as
a measure for describing the behavior of EEG signals, since a noisy activity will have
a broadband spectrum and consequently a high entropy, and on the other side, more
ordered activity as a sinusoidal signal will have lower entropy. Then, WS gives a new
approach to the measure and quantication of the order of a system, its physiological interpretation
being very interesting due to its relation with tuning of cell groups involved
in the generation of the EEG signal.
Entropy in signal analysis
The concept of entropy emerged last century as a useful state function applied to
the study of the thermodynamic of gases (Feynman, 1964). Furthermore, entropy was
related with the order of a system and its applications rapidly expanded to several disciplines
due to its very interesting meanings. One important milestone was the introduction
of the theory of communication (Shannon, 1948 see also Feynman, 1996) relating
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