Biomedical Engineering Reference
In-Depth Information
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(a)
Frequency
(b)
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FIGURE 11.23 Low-pass and high-pass filtered noise signal. (a and b) Gray lines show the power spec-
trum of the input signal. (a) Low-pass filtered noise power spectrum is shown as black. (b) High-pass filtered
noise power spectrum is shown as black.
11.7 SIGNAL AVERAGING
Biological signal measurements are often confounded by measurement noise. Variability
in the measurement of a signal often makes it difficult to determine the signal characteris-
tics, making it nearly impossible to obtain a reliable clinical diagnosis.
Many classes of biological signals are modeled as the sum of an ideal noiseless signal
component,
x
(
t
), and separate independent noise term,
n
(
t
):
x i ð t Þ¼ x ð t Þþ n i ð t Þ:
ð
11
:
49
Þ
The signal,
x i
(
t
), corresponds to the “measured”
i
-th trial or
i-
th measurement of the signal.
Note that the
i-
th measurement contains both a deterministic component,
x
(
t
), and a random
or stochastic noise term,
). Although the deterministic component of the signal is fixed from
trial to trial, the noise term represents intrinsic variability, which may arise from a number of
separate sources. The
n i
(
t
th measurement can therefore exhibit significant trial-to-trial variability
because the random component,
i-
), is different across consecutive trials. As an example, a
measurement ECG (electrocardiogram) electrode can pick up extraneous signals from the
muscles, lungs, and even the internal electronics of the recording devices (e.g., 60 cycle noise
from the power supply). The activity of these signals is unrelated to the activity of the beating
heart, and it therefore shows up in the signal measurement as noise. Other unpredictable
changes in the activity of the heartbeat, such as from the caffeine jolt after drinking an espresso,
could also show up in a measurement and be interpreted as noise to an uninformed observer.
We have already examined one possible way to separate out the signal term from the
noise term by filtering the signal with an appropriately designed filter. Appropriate filter-
ing allows one to clean up the signal, thus improving the quality of signal and the diagnos-
tic reliability in clinical settings. If the spectrum of the noise and signal components do not
overlap in the frequency domain, one can simply design a filter that keeps or enhances the
desired signal term,
n i (
t
). While this is a simple
and useful way of cleaning up a signal, this approach does not work in many instances
because the biological signal and noise spectrums overlap.
x(t)
, and discards the unwanted noise term,
n i
(
t
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