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FIgURE 1.4: A comparison of the scales of electrophysiological recording methodologies.
If one analyzes the time course of one channel of data collected from the scalp (EEG), the
signal time structure is very complex as shown in Figure 1.5 a [ 41 ], reminding us of a nonconvergent
dynamic system, or outputs of complex systems excited by bursty white noise. One of the character-
istics is the rapid fluctuations observed in the signals, which, in the parlance of time series analysis,
represents nonstationary phenomena and can depend upon behavioral statistics. Characterizing and
extracting features from the EEG with conventional modeling is, therefore, very difficult, and the
large number of publications addressing a myriad of methods well exemplifies the difficulty and
suggests that the field is still seeking a good methodology to describe brain waves [ 42-44 ]. The
EEG is called a macroscopic measure of brain activity, and its analysis has been shown to correlate
with cognitive state [ 45 ] and brain diseases such as epilepsy [ 46 ]. The signal is created by a spatial
temporal average of the pulse to amplitude conversion created when billions of pulses of current
(the spike trains) are translated into voltage by the cortical tissue impedance and recorded by a
1-cm diameter electrode. The EEG frequency band extends from 0.1 to approximately 200 Hz,
with a 1/ f type of spectra (suggesting a scale free origin) and spectral peaks concentrated at a handful
of frequencies where the EEG rhythms exist (delta, theta, alpha, sigma, beta, and gamma). Before
 
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