Information Technology Reference
In-Depth Information
http://fraclab.saclay.inria.fr/
.
Below, the dyadic grid is presented, containing the
absolute value of the discrete wavelet coef
cients of the above signal. The high
coef
cients values are in red and the low values in blue. In Fig.
9.12
, the second
level of decomposition, related to low frequencies, contains high absolute coeffi-
-
cients values on the complete signal. The
fifth scale contains mid-range value
coef
cients in the last part of the signal. Finally, the last scale allows to visualize the
high frequency content appearing at the beginning and at the end of the signal.
9.4.2 Signal Energy
Wavelet decomposition can also be used to calculate the energy of a signal for each
level of decomposition. Thus, the energy
e
j
2
of the signal
X
in the scale
j
is given by:
2
j
1
e
j
¼
x
j
;
k
; 8
j
2f
1
; ...
2
j
1
g
ð
9
:
3
Þ
k
¼
1
In other words, from the dyadic grid, the energy associated with the scale
j
(decomposition level
j
) is equal to the sum of the squares of the coef
cients of the
line
j
. The use of signal leads to a loss of the temporality information. It is also
possible to obtain this result using a Fourier transform; however, the DWT provides
more opportunities for further work. For example, the wavelet decomposition could
be useful if the temporal evolution of the frequency content of signals is investi-
gated in a future work.
9.5
Examples of Feature Extraction
9.5.1 Slope Criterion
For a given participant
i
(
i
=1,
…
, 13) in a given state (normal or relaxed), each
electrode
m
(
m
=1,
…
, 58) provides a signal
X
m
. A discrete dyadic wavelet
decomposition
is
performed
on
this
signal
by
considering
15
scales
(15
¼
log
2
ð
46
;
000
b
cÞ
, where 46,000 is the number of points in each 3 min EEG
signals and where
cients obtained, the energy
of the signal is calculated for each scale. Figure
9.13
presents these energies as a
function of frequency.
The Alpha waves are between 8 and 12 Hz. Thus, according to the literature,
only the energies calculated for 4, 8, and 16 Hz are used (black circles in Fig.
9.13
).
Then, a simple regression is performed (dotted line in Fig.
9.13
), and the slope is
retained. This coef
bc
is the integer part). From the coef
cient is representative of the evolution of signal energy in the
frequency considered. By repeating this process for each electrode, a feature of 58
coef
cients (one per electrode) is obtained for an individual in a given state. Thus, a
matrix of size 26
×
58 is obtained, representing the slope criterion.
