The Effects of Data Padding Techniques on Continuous Relative-Phase Analysis Using the Hilbert Transform

Continuous relative phase (CRP) analysis using the Hilbert transform is prone to end effects. The purpose was to investigate the impact of padding techniques (reflection, spline extrapolation, extraneous data, and unpadded) on end effects following Hilbert-transformed CRP calculations, using sinusoidal, nonsinusoidal, and kinematic data from a repeated sit-to-stand-to-sit task in adults with low back pain (n = 16, mean age = 30 y). CRP angles were determined using a Hilbert transform of sinusoidal and nonsinusoidal signals with set phase shifts, and for the left thigh/sacrum segments. Root mean square difference and true error compared test signals with a gold standard, for the start, end, and full periods, for all data. Mean difference and 95% bootstrapped confidence intervals were calculated to compare padding techniques using kinematic data. The unpadded approach showed near-negligible error using sinusoidal data across all periods. No approach was clearly superior for nonsinusoidal data. Spline extrapolation showed significantly less root mean square difference (all periods) when compared with double reflection (full period: mean difference = 2.11; 95% confidence interval, 1.41 to 2.79) and unpadded approaches (full period: mean difference = -15.8; 95% confidence interval, -18.9 to -12.8). Padding sinusoidal data when performing CRP analyses are unnecessary. When extraneous data have not been collected, our findings recommend padding using a spline to minimize data distortion following Hilbert-transformed CRP analyses.