Effect of normalization and phase angle calculations on continuous relative phase

Abstract

The purpose of this investigation was to determine if phase plot normalization and phase angle definitions would have an affect on continuous relative phase calculations. A subject ran on a treadmill while sagittal plane kinematic data were collected with a high-speed (180 Hz) camera. Segmental angular displacements and velocities were used to create phase plots, and examine the coordination between the leg and thigh. Continuous relative phase was calculated with a combination of two different amplitude normalization techniques, and two different phase angle definitions. Differences between the techniques were noted with a root mean square (RMS) calculation. RMS values indicated that there were differences in the configuration of the non-normalized and normalized continuous relative phase curves. Graphically and numerically, it was noted that normalization tended to modify the continuous relative phase curve configuration. Differences in continuous relative phase curves were due to a loss in the aspect ratio of the phase plot during normalization. Normalization tended to neglect the nonlinear forces acting on the system since it did not maintain the aspect ratio of the phase plot. Normalization is not necessary because the arc tangent function accounts for differences in amplitudes between the segments. RMS values indicated that there were profound differences in the continuous relative phase curve when the phase angle was normalized and a phase angle was calculated relative to the right horizontal axis.