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Comparing Methods to Denoise COP Signals
The source for simulating naturalistic reference signals was the signals obtained by a force platform
(Dinascan 600M, IBV, Valencia, Spain) at a sampling rate of 180 Hz, from a population of fourteen
subjects, who performed sixteen trials each of manual lifting and lowering tasks in an experiment
described in detail in § 3.5. In total 224 were obtained. The first forty harmonics were used to
approximate the COP reference signals, ensuring that the reconstructed signals are practically bandlimited to 40 f0 (i.e., Fourier transform is zero outside). Original signals were demeaned before be
transformed into Fourier series. Then, the reconstructed signals were decimated by a factor of 6
using an FIR filter of order 30 to match the noise sample rate of 30 Hz. The duration of the new
signals is of 30 sec, with resolution f o =
30 ,
and cut-off frequency = 1.33 Hz. The experimental
obtained noise added to the reconstructed signals was generated by measuring different static
loads placed at the geometrical center of the top plate of the force platform at sampling rate of
30 Hz for a period of 5 sec. In total 120 noise signals were generated, demeaned, and stored. To
check whether the experimental obtained “zero-mean” noise can be characterized as Gaussian
white noise (GWN), we examine independence (Box-Pierce and Ljung-Box tests) and normality
(Anderson-Darling and Shapiro-Wilks tests) of the time-series. Six noise signals was then pooled
randomly, combined in random order, and added to the reconstructed reference signals to simulate
COP registrations (Fig. B.9). In total 26880 signals were generated, superimposed with additive
non-stationary noise. Three different denoise procedures were compared: low-pass filtering with a
fourth-order zero-phase-shift Butterworth filter with cut-off frequency found following the residual
analysis procedure (Winter, 2009), by quintic splines using the generalized crossed-validation
natural splines smoothing algorithm (GCVSPL) (Woltring, 1986), and by quintic splines according
to the “True Predicted Mean-squared Error” of Woltring (1986) following the proposed uncertainty
Results and Discussion
Noise Test
The results showed that for Fz = constant the noise of the COP signal can be modelled as additive,
zero-mean “white noise”. Different sampling rates influence the COP noise. This is obvious for the
COP signals that were registered with different (low - very high) sampling rates (Fig. B.10). For
example, the variances of the raw COP data for different sampling rates are COP M L RAW -30Hz =
0.54 mm2 , COP M L RAW -230Hz = 0.59 mm2 , COP M L RAW -500Hz = 0.61 mm2 , and COPAP RAW -30Hz
= 1.10 mm2 , COPAP RAW -230Hz = 1.20 mm2 , COPAP RAW -500Hz = 1.30 mm2 . However, for a
narrower frequency interval the assumption that the sampling rate do not influence the COP noise
can be considered as correct. Notwithstanding, the noise elimination, was higher after oversampling
spread the power over higher frequencies. The variance of the COP signals after low-pass filtering
is COPAP BT W -30Hz = 0.24 mm2 , COPAP BT W -230Hz = 0.05 mm2 , COPAP BT W -500Hz = 0.03 mm2
and COP M L BT W -30Hz = 0.15 mm2 , COP M L BT W -230Hz = 0.03 mm2 , COP M L BT W -500Hz = 0.02
mm2 (Fig. B.11). Other studies have also been shown that cut-off frequency and sampling rate
influence stabilometric parameters (Schmid et al., 2002; Scoppa et al., 2013). However, our