Introduction to Sports Biomechanics: Analysing Human Movement ...

INTRODUCTION TO SPORTS BIOMECHANICS
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realised through cross-validated quintic splines. The first or last of these are used in
most commercial quantitative analysis packages. Details of these three techniques are
included in Appendix 4.1 for interested readers.
Quintic splines appear to produce more accurate first and second derivatives than
most other techniques that are commonly used in sports biomechanics. The two
filtering techniques (Fourier truncation and digital filters) were devised for periodic
data, where the pattern of movement is cyclical, as in Figure 4.8(a). Sporting
activities that are cyclic, such as running, are obviously periodic, and some others
can be considered quasi-periodic. Problems may be encountered in trying to filter
non-periodic data, although these may be overcome by removing any linear trend
in the data before filtering; this makes the first and last data values zero. The
Butterworth filter often creates fewer problems here than Fourier truncation, but
neither technique deals completely satisfactorily with constant acceleration motion,
as for the centre of mass when a sports performer is airborne.
The main consideration for the sports biomechanist using smoothing or filtering
routines is a rational choice of filter cut-off frequency or spline smoothing
parameter. A poor choice can result in some noise being retained if the filter cut-off
frequency is too high, or some of the signal being rejected if the cut-off frequency is
too low. As most human movement is at a low frequency, a cut-off frequency of
between 4 and 8 Hz is often used. Lower cut-off frequencies may be preferable for
slow events such as swimming, and higher ones for impacts or other rapid energy
transfers. The cut-off frequency should be chosen to include the highest frequency
of interest in the movement. As filters are sometimes implemented as the ratio of the
cut-off to the sampling frequency in commercially available software, an appropriate
choice of the latter might need to have been made at an earlier stage.
The need for data smoothness demands a minimum ratio of the sampling to cut-off
frequencies of 4:1, and preferably one as high as 8:1 or 10:1. The frame rate used
when video recording, and the digitising rate (the sampling rate), must allow for
these considerations.
The use of previously published filter cut-off frequencies or manual adjustment of
the smoothing parameter is not recommended. Instead, a technique should be used
that involves a justifiable procedure to take into account the peculiarities of each
new set of data. Attempts to base the choice of cut-off frequency on some objective
criterion have not always been successful. One approach is to compare the RMS
difference between the noisy data and that obtained after filtering at several different
cut-off frequencies with the standard deviation obtained from repetitive digitisation
of the same anatomical point. The cut-off frequency should then be chosen so that
the magnitudes of the two are similar. Another approach is called residual analysis,
in which the residuals between the raw and filtered data are calculated for a range of
cut-off frequencies: the residuals are then plotted against the cut-off frequency, and
the best value of the latter is chosen as that at which the residuals begin to approach
an asymptotic value, as in Figure 4.9; some subjective judgement is involved in
assigning the cut-off frequency at which this happens.