SIGNAL PROCESSING - Biomechanics and Motor Control of Human Movement - page 35

for a subject standing quietly for 137 seconds (8192 samples @ 60 Hz). Note
that the FFT plots the amplitude of each harmonic from 0.0073 Hz to 1 Hz.
Also note the dominant low frequency components of both COM and COP
below 0.2 Hz. The length of record must be at least a minute or longer.
This long record may be compromised when studying patients with balance
disorders because they may not be able to stand quietly for that length of
time. However, for studies on normal subjects Carpenter, et al. (2001) found
that records of at least one minute were required for acceptable reliability.
2.2.4.4 Analog and Digital Filtering of Signals — Noise and Movement
Artifacts. The basic approach can be described by analyzing the frequency
spectrum of both signal and noise. Figure 2.16 a shows a schematic plot of a
signal and noise spectrum. As can be seen, the signal is assumed to occupy
the lower end of the frequency spectrum and overlaps with the noise, which
is usually higher frequency. Filtering of any signal is aimed at the selective
rejection, or attenuation, of certain frequencies. In the preceding case, the
obvious filter is one that passes, unattenuated, the lower-frequency signals,
while at the same time attenuating the higher-frequency noise. Such a filter,
called a low-pass filter , has a frequency response as shown in Figure 2.16 b .
The frequency response of the filter is the ratio of the output X o (f ) of the filter
to its input X i (f ) at each frequency present. As can be seen, the response at
lower frequencies is 1.0. This means that the input signal passes through
the filter unattenuated. However, there is a sharp transition at the cutoff
frequency f c so that the signals above f c are severely attenuated. The net result
of the filtering process can be seen by plotting the spectrum of the output
signal X o (f ) as seen in Figure 2.16 c . Two things should be noted. First,
the higher-frequency noise has been severely reduced but not completely
rejected. Second, the signal, especially in the region where the signal and
noise overlap (usually around f c ) is also slightly attenuated. This results in
a slight distortion of the signal. Thus, a compromise has to be made in the
selection of the cutoff frequency. If f c is set too high, less signal distortion
occurs, but too much noise is allowed to pass. Conversely, if f c is too low, the
noise is reduced drastically, but at the expense of increased signal distortion.
A sharper cutoff filter will improve matters, but at an additional expense.
In digital filtering, this means a more complex digital filter and, thus, more
computer time.
The first aspect that must be assessed is what the signal spectrum is as
opposed to the noise spectrum. This can readily be done, as is seen in the har-
monic analysis for 20 subjects presented in Figure 2.17. Here is the harmonic
content of the vertical displacement of the toe marker in natural walking
(Winter et al., 1974). The highest harmonics were found to be in the toe
and heel trajectories, and it was found that 99.7% of the signal power was
contained in the lower seven harmonics (below 6 Hz). Above the seventh
harmonic, there was still some signal power, but it had the characteristics of
“noise.” Noise is the term used to describe components of the final signal