GRUPOS DE DISCUSIÓN PADRES

The identification of cut-off frequency for filtering biomechanical data is a prevalent issue in biomechanics research. Because of a region of signal and noise overlap, there is a need to find the best compromise between noise reduction and signal elimination (Winter, 2009). A fourth-order low-pass Butterworth filter was used in this thesis. The decision to use a fourth-order Butterworth filter over other methods (e.g. Fourier Series, Hatze, 1981; Jackson, 1979; Spline smoothing, Woltring, 1985) was based on its widespread use within biomechanics (Ball, 2008; Ball, 2011b; Ball, Best, & Wrigley, 2001; Ball, Best, & Wrigley, 2003a; Ball, Best, & Wrigley, 2003b; Dörge, Bull-Andersen, Sørensen, & Simonsen 2002; Nunome, Ikegami, Kozakai, Apriantono, & Sano, 2006; Panchuk et al., 2013; Werner et al., 2006).

There are a number of methods, which have been used in the determination of optimal cut-off frequency for Butterworth filters. These methods include the use of: visual inspection (Ball, 2008; Ball, 2011b; Ball & Best, 2007); previously published values (Ball, 2011b); automated methods (Yu, 1989; Yu et al., 1999; Winter, 2009; Challis, 1999); spectral analysis (Ball et al., 2001) and inspecting the influence of different cut-offs on parameters of interest (Ball & Best, 2007; Ball, 2008). The limitations of these methods include the lack of objectivity (visual inspection), not accounting for variations in analysis protocols and data quality (previously published values), over-smoothing at high frequencies (residual analysis), and not accounting for variation in the quality of raw data sets collected at the same sampling frequency (estimations based on sampling frequency). Additionally, Giakas & Baltzopoulos

(1997b) suggested that estimation for optimal cut-off frequency should not be purely based on displacement data.

Giakas and Baltzopoulos (1997a) and Ball et al. (2001) provide evidence that there is no optimal solution for the selection of cut-off frequency to filter biomechanical data. Giakas and Baltzopoulos (1997a) advise researchers to take the assumptions and limitations of the method(s) employed into account. Ball et al. (2001) suggested that both objective (automated methods) and subjective (visual inspection of curves) should be considered when deciding on a smoothing cut-off. Based on the recommendations of these authors, the determination of the cut-off frequency used to filter biomechanical data in this thesis was based on a combination of residual analysis (objective), visual inspection of resulting curves (subjective), and spectral analysis to assess system noise and the effect on parameters of interest using a range of cut-offs in support. A

description of the process is provided in Appendix B (Winter, 2009).

Residual analysis was selected as one methodology because of its common application within sport biomechanics research (drop-punt kicking, Ball, 2008; golf, Ball & Best, 2007; shooting, Ball et al., 2003a; Ball et al., 2003b; soccer kicking, Dörge et al., 2002; catching, Panchuk et al., 2013) and because of the ability to gain data specific cut-off information. The main limitation of this method is that is has been suggested to over-smooth data (Giakas & Baltzopoulos, 1997a; Yu et al., 1999). Giakas and Baltzopoulos (1997a) found that residual analysis tended to under estimate the cut- off frequency of displacement data in comparison with the five other methods assessed (e.g. power spectrum analysis, regularised Fourier series); however, residual analysis did not perform as poorly for first or second derivative data.

Yu et al. (1999), also demonstrated that the cut-off value determined through residual analysis was below the optimum cut-off, especially for higher frequencies (Figure 8.2).

Figure 8.2: Figure replicated from Yu et al. (pg. 327, 1999) – The relationship between the optimum cut-off frequency derived from residual analysis.

A comparison of four methods used on three different datasets, however, demonstrated that other methods also indicate low values (Ball et al., 2001). Although Yu and colleagues (1999) indicate that residual analysis may over smooth and that their method more closely reflects the optimal cut-off frequency, in some data sets, the cut- off determined by Yu et al. (1999) was lower than other methods (Table 8.5).

Table 8.5

Table replicated from Ball, Best and Wrigley (pg. 1, 2001) – The optimal cut-off frequency determined by four methods tested

Golf Swing Shooting Walking

Front foot Back foot

CPx CPy CPx CPy CPx CPy x y

Challis (1999) 11.0 17.5 11.5 34.5 9.5 32.5 12.5 12.5 Yu et al. (1999) 24.7 24.6 25.3 24.7 7.5 9.7 3.0 3.5 Winter (1990) 14.0 15.0 14.0 14.0 6.0 5.5 10.0 4.0

To substantiate the use of residual analysis, findings were compared against the method proposed by Yu et al. (1999). For a 100 Hz sample rate, the optimal cut-off according to Yu’s automated selection equation is 9 Hz (Yu, 1989). The full protocol for the estimation of optimum cut off frequency requires calculation and use of the relative mean residual. Using this process, the calculation indicated that data should be filtered at 6 Hz, which was lower than the 7 Hz average selected through residual analysis.

Although objective determination of the optimal cut-off frequency is warranted, given the discrepancies of the varying methods, using one method alone in preference to another method has been suggested to add subjectivity (Ball et al., 2001) and therefore evaluation of a number of methods (residual analysis, visual inspection, spectral

analysis and comparison of effects on parameters of interest) provides a strong basis for the choice of cut-off in this thesis.

The evaluation of how cut-off frequency affects different outcome measures is one consideration, which is rarely addressed in the literature (c.f. Ball et al., 2001; Ball, 2008). As Yu et al. (1999) suggested that the optimal cut-off frequency determined through residual analysis (7 Hz) would over smooth the data; it was compared with the optimal cut-off determined by Yu’s automated calculation (9 Hz, Yu, 1989). Firstly a comparison of the squared residuals at 7 and 9 Hz was completed. The difference between these two cut-off frequencies ranged between 1.0 x 10-5 and 2.0 x 10-6, suggesting little meaningful difference between the two cut-off frequencies. Secondly, two of the key parameters that were identified as having the strongest correlation in Study 2 were reassessed using a 9 Hz cut-off.

This was performed using a random subset of half of the participants in order to assess the difference between the values produced using 7 Hz versus 9 Hz as the filter cut-off frequency (Table 8.6).

Table 8.6

Difference in two key parameters (Hand speed and shoulder angular velocity) when filtered at 7 and 9 Hz

Participant Hand speed (m/s)

Shoulder Angular Velocity (°/s) 7 Hz 9 Hz 7 Hz 9 Hz 1 10.4 10.6 221 222 2 8.2 8.3 90 91 3 9.2 9.4 212 211 4 9.7 9.9 148 150 5 10.2 10.3 612 619 6 8.6 8.9 176 176 7 10.4 10.5 352 354 8 10.3 10.5 225 224 9 9.4 9.6 204 206 Average 9.6 9.8 249 250

The average differences in hand speed and shoulder angular velocity were 0.2 m/s and 1 °/s, respectively. In addition, the difference in the correlation coefficient between these two parameters for 7 Hz and 9 Hz was 0.0129 and did not change the effect size (r = 0.55 for 7 Hz, r = 0.54 for 9 Hz) of the correlation coefficient between these two parameters. Furthermore, the same conclusions would have been reached had either cut-off been used. This finding demonstrates, though there is a need to choose an appropriate cut-off frequency, that there is a tolerance level to which it may not

functionally affect the data.

In summary, the use of 7 Hz as the cut-off frequency for filtering the biomechanical data was built upon the advice of Ball et al. (2001) and Giakas and Baltzopoulos (1997a). Four methods were used in the determination of this cut-off frequency (see Appendix B). Comparing the effect of cut-off frequency on parameters

of interest is less commonly used, but was a useful step in this thesis to help validate the selection of the cut-off frequency.