Order error in the calculation of continuous relative phase

The aims of this study were to demonstrate "order error" in the calculation of continuous relative phase (CRP) and to suggest two alternative methods-(i) constructing phase-plane portraits by plotting position over velocity; and (ii), the Hilbert transform-to rectify it. Order error is the change of CRP order between two degrees of freedom (e.g., body segments) when using the conventional method of constructing phase-plane portraits (i.e., velocity over position). Both sinusoidal and non-sinusoidal simulated signals as well as signals from human movement kinematics were used to investigate order error and the performance of the two alternative methods. Both methods have been shown to lead to correct results for simulated sinusoidal and non-sinusoidal signals. For human movement data, however, the Hilbert transform is superior for calculating CRP.