SIGNAL PROCESSING - Biomechanics and Motor Control of Human Movement - page 32

Figure 2.12 Sampling of two signals, one at a proper rate, the other at too low a
rate. Signal 2 is sampled at a rate less than twice its frequency, such that its sampled
amplitudes are the same as for signal 1. This represents a violation of the sampling
theorem and results in an error called aliasing .
this effect. Both signals are being sampled at the same interval T . Signal 1
is being sampled about 10 times per cycle, while signal 2 is being sampled
less than twice per cycle. Note that the amplitudes of the samples taken from
signal 2 are identical to those sampled from signal 1. A false set of sampled
data has been generated from signal 2 because the sample rate is too low — the
sampling theorem has been violated.
The tendency of those using film is to play it safe and film at too high
a rate. Usually, there is a cost associated with such a decision. The initial
cost is probably in the equipment required. A high-speed movie camera can
cost four or five times as much as a standard model (24 frames per second).
Or a special optoelectric system complete with the necessary computer can
be a $70,000 decision. In addition to these capital costs, there are the higher
operational costs of converting the data and running the necessary kinematic
and kinetic computer programs. Except for high-speed running and athletic
movements, it is quite adequate to use a standard movie or television camera.
For normal and pathological gait studies, it has been shown that kinetic and
energy analyses can be done with negligible error using a standard 24 - frame
per second movie camera (Winter, 1982). Figure 2.13 compares the results
of kinematic analysis of the foot during normal walking, where a 50-Hz
film rate was compared with 25 Hz. The data were collected at 50 Hz, and
the acceleration of the foot was calculated using every frame of data, then
reanalyzed again, using every second frame of converted data. It can be seen
that the difference between the curves is minimal; only at the peak negative
acceleration was there a noticeable difference. The final decision as to whether
this error is acceptable should not rest in this curve, but in your final goal.
If, for example, the final analysis was a hip and knee torque analysis, the
acceleration of the foot segment may not be too important, as is evident from