Fig. 2

Sample result of the phase difference estimations on simulated signals. A 60-s sample result of phase difference estimations on two triangular signals s ₃(t) and s ₄ (t) with correlated (a, b) and uncorrelated (f, g) noises and phase difference θ ₀ = 20° done by using the loop analysis (c, h), IPD method (d, i), and APEP (e, j). The frequency of s ₃(t) and s ₄ (t) was set to 0.2 Hz. The dashed line represent the gold standard (i.e., θ ₀ = 20°). The absent of data for loop analysis in 0–2.5 and 58.5–60 s was caused by the incompleteness of cycles. The loop analysis in fact only generates one output value per cycle of breathing at the end of each cycle. The straight lines drawn in the panel c throughout the beginning to the end of each cycle are manually produced after the analysis. Loop analysis only has one value per cycle in the end of cycles. The phase differences of the cycles are filled with that output value manually in order to make the figure more comprehensive