Introduction to Sports Biomechanics: Analysing Human Movement ...

APPENDIX 4.1 DATA SMOOTHING AND FILTERING
Digital low-pass filters
Digital low-pass filters are widely used to remove, or filter, high-frequency noise from
digital data. Butterworth filters (of order 2n where n is a positive integer) are often used
in sports biomechanics, because they have a flat passband, the band of frequencies that
is not affected by the filter (Figure 4.16). However, they have relatively shallow cut-offs.
This can be improved by using higher-order filters, but round-off errors in computer
calculations can then become a problem. They also introduce a phase shift, which must
be removed by a second, reverse filtering, which increases the order of the filter and
further reduces the cut-off frequency.
Butterworth filters are recursive; that is, they use filtered values of previous data
points as well as noisy data values to obtain filtered data values. This makes for
faster computation but introduces problems at the ends of data sequences, at which
filtered values must be estimated. This can mean that extra frames must be digitised at
each end of the sequence and included in the data processing; these extra frames then
have to be discarded after filtering. This can involve unwelcome extra work for the
movement analyst; other solutions include various ways of padding the ends of the data
sets.
The main decision for the user, as with Fourier series truncation, is the choice of
cut-off frequency (discussed on pages 133–7). The filtered data are not obtained in
analytic form, so a separate numerical differentiation process must be used. Although
Butterworth filtering appears to be very different from spline fitting (see below), the
two are, in fact, closely linked.
Figure 4.16 Low-pass filter frequency characteristics.
QUANTITATIVE ANALYSIS OF MOVEMENT
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