Application of singular spectrum analysis to the smoothing of raw kinematic signals  F.J. Alonso, J.M.Del Castillo, P. Pintado  Journal of Biomechanics  Volume 38, Issue 5, Pages 1085-1092 (May 2005) DOI: 10.1016/j.jbiomech.2004.05.031

Fig. 1 Noisy displacement (Signal 1) recorded using a motion capture system. Journal of Biomechanics 2005 38, 1085-1092DOI: (10.1016/j.jbiomech.2004.05.031)

Fig. 2 Original noisy displacement (Signal 4) recorded using a motion capture system. Journal of Biomechanics 2005 38, 1085-1092DOI: (10.1016/j.jbiomech.2004.05.031)

Fig. 3 Singular spectrum (in logarithmic scale) of Signal 1, obtained with a window length L = 40. Journal of Biomechanics 2005 38, 1085-1092DOI: (10.1016/j.jbiomech.2004.05.031)

Fig. 4 Individual reconstruction of the five leading components (plotted in different scales) obtained from the SVD of Signal 1, using a window length L = 40. Journal of Biomechanics 2005 38, 1085-1092DOI: (10.1016/j.jbiomech.2004.05.031)

Fig. 5 (a) Noisy displacement (dotted line) and SSA-smoothed displacement (continuous line) corresponding to Signal 1. (b) Residual signal defined as the difference between the original and smoothed signals. (c) Zoom in the neighbourhood of t = 1.77s to appreciate the slight difference between the original and SSA-smoothed signals. Journal of Biomechanics 2005 38, 1085-1092DOI: (10.1016/j.jbiomech.2004.05.031)

Fig. 6 (a) Acceleration calculated from Signal 1 original displacement data. (b) Acceleration calculated from Signal 1 after having been smoothed using SSA. (c) Acceleration calculated from Signal 1 after having been passed through a 4Hz cut frequency Butterworth filter. Journal of Biomechanics 2005 38, 1085-1092DOI: (10.1016/j.jbiomech.2004.05.031)

Fig. 7 Acceleration obtained from reference signal 2 (continuous line) and acceleration calculated from SSA-smoothed displacement data (dotted line). Journal of Biomechanics 2005 38, 1085-1092DOI: (10.1016/j.jbiomech.2004.05.031)

Fig. 8 Reference angular acceleration corresponding to Signal 3 (continuous line) and acceleration calculated from angular displacement data smoothed with a sequential SSA decomposition (dotted line). Journal of Biomechanics 2005 38, 1085-1092DOI: (10.1016/j.jbiomech.2004.05.031)

Fig. 9 (a) Acceleration calculated from Signal 4 original displacement data (dashed line) and acceleration measured by the accelerometer (continuous line). (b) Acceleration calculated from displacement reconstructed using the sixteen leading components (dotted line) and acceleration measured by the accelerometer (continuous line). (c) Acceleration calculated from displacement reconstructed using the five leading components (dotted line) and acceleration measured by the accelerometer (continuous line). Journal of Biomechanics 2005 38, 1085-1092DOI: (10.1016/j.jbiomech.2004.05.031)