Figure 9
From: An extended Hilbert transform method for reconstructing the phase from an oscillatory signal
Detecting the phase shift from an oscillatory signal. (a) Observed signal x(t) (Eq. 18). (b) Phase-modulation u(t). (c,d) Dependence of the phase reconstruction error on the phase shift amplitude in (c) and the phase shift duration in (d). We plotted the mean and standard deviation of the mean squared errors (MSEs) calculated from 100 trials in (c,d). Parameters were set as the effective frequency \(\hat{\omega }_1= 2\pi \), the noise variance \(\sigma = 0.1\), the shift amplitude \((\hat{\omega }_2- \hat{\omega }_1) \Delta _T= 0.5\) in (a,b,d), and the the shift duration \(\Delta _T = 0.2\) in (a–c).
