Introduction to Sports Biomechanics: Analysing Human Movement ...

QUANTITATIVE ANALYSIS OF MOVEMENT
Figure 4.18 Simple example of: (a) noisy data in the frequency domain; (b) same data in the time domain after removal of
noise by filtering by Fourier series truncation.
simplified data of Figure 4.18(a), if the cut-off frequency was, say, 4 Hz, then the
second frequency term would be rejected as noise.
In this simplified case, the noise would have been removed perfectly, as the time
domain signal of Figure 4.18(b) demonstrates. There would be no resulting errors in
the velocities and accelerations. The major decision here concerns the choice of cut-off
frequency, and similar principles to those described on pages 133–7 can be applied.
Unlike digital filters, the cut-off can be infinitely steep, as in Figure 4.16, but this is not
necessarily the case. The filtered data can be represented as an equation and can be
differentiated analytically. This technique requires the raw data points to be sampled at
equal time intervals, as do digital low-pass filters (see above).
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