Single-Channel EEG Analysis - Quantitative EEG Analysis Methods and Clinical Applications - page 96

10

0

Synthetic signal (EEG+Spikes)

− 10

0 2000 4000 6000 8000 10000 12000

(a)

4

2

Shannon TDE

0

0 2000 4000 6000 8000 10000 12000

(b)

0.4

0.3

Tsallis TDE (q=4.0)

10

0 2000 4000 6000 8000 10000 12000

(c)

Figure 3.30 Sensitivity of time-dependent entropy in describing the transient burst activity: (a) syn-
thetic signal (baseline EEG mixed with three bursts of different amplitudes), (b) time-dependent
Shannon entropy, and (c) time-dependent Tsallis entropy ( q = 4.0). The parameters of the sliding
window are w = 128 samples and Δ = 1 sample.

3.3.3.1 Window Size ( w )
When studying the short spiky component, for a fixed window lag (

), the larger the
window size ( w ), the more windows that will include the spike; that is, window size
( w ) determines the temporal resolution of TDE. A smaller window size results in a
better temporal localization of the spiky signals. Figure 3.31 illustrates the TDE
analysis with different window sizes ( w

Δ

64, 128, and 256) for a typical EEG seg-
ment following hypoxic-ischemic brain injury, punctuated with three spikes. The
TDE results demonstrate the detection of the spikes, but the smaller window size
yields better temporal resolution.
Even though a smaller window size provides better temporal localization for
spiky signals as shown in Figure 3.31, short data will result in an unreliable PDF,
which leads to a bias of entropy estimation and unavoidable errors. By far, however,
there is no theoretical conclusion about the selection of window size. In EEG studies,
we empirically used a 0.5-second window. Figure 3.32 illustrates the Shannon TDE
analysis of typical spontaneous EEG segments ( N

=

1,024 samples) for window sizes
from 64 to 1,024 samples. The figure clearly shows that when the window size is
more than 128 samples, the TDE value reaches a stable value.

=