Introduction to Sports Biomechanics: Analysing Human Movement ...

is non-stationary, when the statistical properties of the signal vary with time.
A high cut-off frequency results in a noisy estimator for stationary activations
and a linear envelope that follows closely the changes in the EMG. Typical values
of the cut-off frequency are around 2 Hz for slow movements such as walking, and
around 6 Hz for faster movements such as running and jumping. Also, SENIAM
recommends that the cut-off frequency used should always be reported along with
the type and order of filter. Most software packages for EMG analysis in sports biomechanics
use a standard fourth-order Butterworth filter (as for filtering kinematic data
in Appendix 4.1).
A development of this approach is the use of an ensemble average calculated over
several repetitions of the movement. This procedure theoretically – for physiologically
identical movements – reduces the error in the amplitude estimation by a factor
equal to the square root of the number of cycles. It is often used in clinical gait analysis
but ignores the variability of movement patterns. It appears inappropriate for fast
sports movements. The recommendations of SENIAM are that, if used, the number of
cycles over which the ensemble average is calculated should be reported along with the
standard error of the mean, to show up any movement variability.
Frequency domain analysis (spectral estimation)
THE ANATOMY OF HUMAN MOVEMENT
Unless the data are explicitly time-limited, as in a single action potential, the
EMG signal can be transformed into the frequency domain (as for kinematic data in
Chapter 4). The EMG signal is then usually presented as a power spectrum (power
equals amplitude squared) at a series of discrete frequencies, although it is often represented
as a continuous curve, as in Figure 6.24. The epoch duration, over which the
transformation of the time domain signal into the frequency domain occurs, which is
recommended by SENIAM is 0.5–1.0 s. Again, these epoch durations considerably
exceed the durations of muscle activity in many fast sports movements.
The central tendency and spread of the power spectrum are best expressed by the use
of statistical parameters, which depend upon the distribution of the signal power over
its constituent frequencies. Two statistical parameters are used to express the central
tendency of the spectrum. These are comparable to the familiar mean and median in
statistics. For a spectrum of discrete frequencies, the mean frequency is obtained
by dividing the sum of the products of the power at each frequency and the frequency,
by the sum of all of the powers. The median frequency is the frequency that divides
the spectrum into two parts of equal power – the areas under the power spectrum to the
two sides of the median frequency are equal. The median is less sensitive to noise than
is the mean. The spread of the power spectrum can be expressed by the statistical
bandwidth, which is calculated in the same way as a standard deviation.
The EMG power spectrum can be used, for example, to indicate the onset of
muscle fatigue. This is accompanied by a noticeable shift in the power spectrum
towards lower frequencies (Figure 6.25) and a reduction in the median and mean
frequencies. This frequency shift is caused by an increase in the duration of the MUAP.
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