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Table 1 Results of phase difference estimation on various simulated signals

From: Instantaneous phase difference analysis between thoracic and abdominal movement signals based on complementary ensemble empirical mode decomposition

θ 0 Sinusoidal signals with correlated noise Triangular signals with correlated noise
IPD Loop analysis APEP IPD Loop analysis APEP
20° 20 ± 0.14 19 ± 0.10*** 20 ± 0.28 20 ± 0.13 15 ± 0.14*** 20 ± 0.37
30° 30 ± 0.22 29 ± 0.17*** 30 ± 0.31 30 ± 0.23 23 ± 0.19*** 30 ± 0.26
50° 50 ± 0.33 49 ± 0.29*** 50 ± 0.70 50 ± 0.27 42 ± 0.33*** 50 ± 0.63
90° 90 ± 0.40 90 ± 0.97 90 ± 0.51 90 ± 0.36 90 ± 1.04* 90 ± 0.60
140° 140 ± 0.44 140 ± 0.63* 140 ± 0.44*** 140 ± 0.34 146 ± 0.63*** 138 ± 0.46***
170° 170 ± 0.49 170 ± 0.63*** 156 ± 0.45*** 170 ± 0.49 172 ± 0.63*** 150 ± 0.57***
θ 0 Sinusoidal signals with uncorrelated noise Triangular signals with uncorrelated noise
IPD Loop analysis APEP IPD Loop analysis APEP
20° 20 ± 0.33 19 ± 0.46*** 27 ± 0.41*** 20 ± 0.34 15 ± 0.40*** 32 ± 0.35***
30° 30 ± 0.34 29 ± 0.49*** 32 ± 0.41*** 30 ± 0.45 23 ± 0.45*** 36 ± 0.49***
50° 50 ± 0.42 49 ± 0.53*** 50 ± 0.69 50 ± 0.36 42 ± 0.60*** 50 ± 0.87**
90° 90 ± 0.34 90 ± 0.71 90 ± 0.44 90 ± 0.35 90 ± 0.95 90 ± 0.44
140° 140 ± 0.30 140 ± 0.43*** 140 ± 0.43 140 ± 0.31 146 ± 0.48*** 140 ± 0.45
170° 170 ± 0.35 169 ± 0.32*** 170 ± 0.32 170 ± 0.35 172 ± 0.33*** 170 ± 0.34***
  1. The results of phase difference estimation done by using IPD, loop analysis, and APEP on simulated time series under different simulation setups. The θ 0 and the estimated phase difference were submitted to one-sample t test
  2. The significant difference between the estimated phase difference and the gold standard θ 0 is denoted by * p < 0.05, ** p < 0.01, *** p < 0.001