Biomedical Engineering Reference
In-Depth Information
that is because of the fact that the FFT is plotting the amplitude at every
single Hz. A more realistic plot of this spectrum is to carry out a moving
average across the full spectrum, and this was done with a 40-point moving
average, which is the “white” curve in Figure 2.19 (b). This moving average
approaches the theoretical constant amplitude across the full spectrum; its
average amplitude is 0.330 and ranges from 0.233 to 0.446. A longer time
domain record than the 2048 points will result in a more constant frequency
plot. Also, it should be noted that some of the individual harmonic amplitudes
are greater than one, and this is not expected from the white noise signal,
which had an amplitude of
1. What is not shown here are the phase angles
of each of the harmonics; each has a different phase angle, so there will be
many cancellations as each harmonic is added.
±
2.3
ENSEMBLE AVERAGING OF REPETITIVE WAVEFORMS
A large number of movements that we study are cyclical in nature and,
therefore, can benefit from a cyclical average of its many variables. Gait
(walking and running) is the most common repetitive movement but cycling,
rowing, and lifting also benefit from such averaged profiles. Both intra- and
inter-subject averaged profile have been reported on a wide variety of kine-
matic, kinetic and EMG variables. The major benefit of such a technique
is that the averaged waveform is more reliable and the variation about the
mean gives us additional information as to the randomness of the variable.
For example, in gait the intra-subject lower limb joint angles have minimal
variability, while the moment profiles at these same joints are quite variable.
This phenomenon has resulted in a covariance analysis, which can readily be
done; we can calculate the mean variance at each of the joints from these
ensemble averages, from which the covariances can be determined. As a
result of those analyses, a total lower limb motor synergy has been identi-
fied, and this is reported in detail in Chapter 11. Such ensemble-averaged
waveforms also form the basis of clinical assessments, where the patient's
profile superimposed on the average for a comparable healthy group provides
a very powerful tool in diagnosing specific motor abnormalities. An example
of such a clinical analysis is presented in the next section, Section 2.3.1.
2.3.1 Examples of Ensemble-Averaged Profiles
Figure 2.20 shows a typical waveform from a clinical gait study of an
above-knee amputee; the ankle, knee, and hip moments of the amputee
(dashed lines) are overlaid on the averaged profiles for 29 young adults
(Winter, 1995). The detailed diagnostics will not be discussed here except
to comment that the deviations from normal of each joint moment are readily
evident, and these differences may lead to altered therapy or adjustments
in the prosthesis. Note the averaged profiles are solid lines with dotted
Search WWH ::




Custom Search