Biomedical Engineering Reference
In-Depth Information
10
Original EEG
5
0
-5
-10
After Blackman
window
-15
-20
-25
Autocorrelation
-30
0
2
4
6
8
10
12
14
16
Time (sec)
(a)
Figure 9.6
(a) An illustration of time-domain-based EEG processing. The top waveform is the origi-
nal signal of anesthetized rat scalp recording following analog antialias filtering with a bandpass of
0.3-30 Hz and digitizing at 256 Hz. The middle tracing demonstrates the effect of windowing on the
original signal. Windowing is a technique employed to reduce distortion from epoch end artifacts in
subsequent frequency domain processing. A window consists of a set of digital values with the same
number of members as the data epoch. In this case, a Blackman window was employed. The window
operation multiplies each data sample value against its corresponding window value, that is, the
resulting waveform
z
(
i
)
x
(
i
)*
w
(
i
) for each value of
i
in the epoch. The bottom tracing is the
autocorrelation function of this epoch of EEG. The autocorrelation provides much of the same infor-
mation as a frequency spectrum in that it can identify rhythmicities in the data. In this case, the stron-
gest autocorrelation is at time
=
0 as might be anticipated, and there are some weak rhythmicities
which taper off as the lag increases above 1 second. (b) Continuing with the same epoch of digitized
EEG, the top two tracings are the real and imaginary component spectra respectively resulting from
the Fourier transform. The middle trace is the phase spectrum, which is classically has been discarded
due to the present lack of known clinically useful correlation. The bottom tracing is the power spec-
trum. It is calculated as the sum of the squared real and imaginary components at each frequency
[i.e., measuring the squared magnitude for each frequency value of the complex spectrum,
X
(
f
)].
Recall that power equals squared voltage. Note that the power spectrum, by reflecting only spectral
magnitude, has explicitly removed whatever phase versus frequency information was present in the
original complex spectrum. From the power spectrum, the QEEG and relative band powers are calcu-
lated as described in the text.
=
2
π
i
4
π
i
⎛
⎜
⎞
⎟
+
⎛
⎜
⎞
⎟
()
042
05
w
i
=
.
−
. cos
08
. cos
Blackman
n
−
1
n
−
1
() () ()
x
i
=
x i
*
w i
for each
i
in the epoch
windowed
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