Phase Estimation of a Single Quasi-Periodic Signal

We propose a method for phase estimation of a single non-parametric quasi-periodic signal. Assuming signal intensities should be equal among samples of the same phase, such corresponding samples are obtained by self-dynamic time warping between a quasi-periodic signal and a signal with multiple-period shifts applied. A phase sequence is then estimated in a sub-sampling order using an optimization framework incorporating 1) a data term derived from the correspondences and 2) a smoothness term of the local phase evolution under 3) a monotonic-increasing constraint on the phase. Such a phase estimation is, however, ill-posed because of combination ambiguity between the phase evolution and the normalized periodic signal, and hence can result in a biased solution. Therefore, we introduce into the optimization framework 4) a bias correction term, which imposes zero-bias from the linear phase evolution. Analysis of the quasi-periodic signals from both simulated and real data indicate the effectiveness and also potential applications of the proposed method.