Biomedical Engineering Reference
In-Depth Information
Pressure Waveforms (mmHg)
Signal Averaged Waveform (mmHg)
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
0
0.1
0.2
0.3
0.4
0
0.1
0.2
0.3
0.4
Time (S)
Time (S)
FIGURE 11.24
A signal-averaged pressure waveform for the data shown in Figure 11.2.
In both cases, note that the averaging helps to preserve the relevant signal features and
remove undesirable noise disturbances.
The blood pressure and ABR examples illustrate signal averaging in the time domain.
For signals that are random in nature, signal averaging in the frequency domain is some-
times preferable. Figure 11.26 shows an EEG signal sampled over the occipital lobe of a
patient. The sampling rate was 16 kHz. EEG analysis is usually done in the frequency
domain, since the presence of different frequencies is indicative of different brain states,
such as sleeping, resting, alertness, and so on. The power at each frequency estimate, which
can be approximated by the square of the Fourier transform, is the measurement of choice.
If a DFT is performed on the data to estimate the power of the frequencies in the signal, the
expected noise in themeasurement is of the same size as the measurement itself. To reduce the
noise variance, a statistical approach must be undertaken. One popular approach is known as
the “Welch” or “periodogram averaging” method. The signal is broken into
L
sections (dis-
joint if possible) of
N
points each. ADFT is performed on each of the
L
sections. The final result
for the
frequencies is then the average at each frequency for the
sections.
N
L
The
data points in the
-th segment are denoted as
N
i
x
i
ð
k
Þ¼
x
ð
k
þð
i
1
Þ
N
Þ
0
k
N
1, 1
i
L
