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

ENTROPY
Thermodynamics
Signal analysis
Situation A
Order
=
low entropy
Fourier
Situation B
Disorder
=
high entropy
Fourier
Figure 30: Entropy in thermodynamics and in signal analysis.
These disadvantages of the Fourier Transform are partially resolved by using the
Gabor Transform (Powell and Percival already dened a time evolving entropy from
the Gabor Transform by using a Hanning window). Nevertheless, as already discused in
previous chapters, the selection of the window size is critical due to the UncertaintyPrinciple
and this limitation becomes important when the signal has transient components
localized in time as in ERPs.
Wavelets haveavarying window size, thus allowing a better time-frequency resolution
for all the scales. Consequently, a further improvement to the spectral entropy is to
dene the entropy from the Wavelet transform. In the latter case, the time evolution of
the frequency patterns can be followed with an optimal time-frequency resolution.
In this chapter, I will rst introduce the denition of the Wavelet-entropy and then I
will describe its application to the study of ERPs (Quian Quiroga et al., 1999a,b Rosso
et al., 1998).
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