Computation of continuous relative phase and modulation of frequency of human movement

Continuous relative phase measures have been used to quantify the coordination between different body segments in several activities. Our aim in this study was to investigate how the methods traditionally used to compute the continuous phase of human rhythmic movement are affected by modulations of frequency. We compared the continuous phase computed method with the traditional method derived from the position-velocity phase plane and with the Hilbert Transform. The methods were tested using sinusoidal signals with a modulation of frequency between or within cycles. Our results showed that the continuous phase computed with the first method results in oscillations in the phase time-series not expected for a sinusoidal signal and that the continuous phase is overestimated with the Hilbert Transform. We proposed a new method that produces a correct estimation of continuous phase by using half-cycle estimations of frequency to normalize the phase planes prior to calculating phase angles. The findings of the current study have important implications for computing continuous relative phase when investigating human movement coordination.