Instantaneous phase tracking of oscillatory signals using emd and Rao-Blackwellised particle filtering

A new method for instantaneous phase tracking of oscillatory signals in a narrow band frequency range is proposed. Empirical mode decomposition (EMD), as an adaptive and data-driven method for analyzing non-linear and non-stationary time series, is applied to a mixture of signals. Then, one of the resulted intrinsic mode functions (IMFs) is used for estimating the instantaneous phase of the signal in a certain frequency band. Since by applying EMD to the noisy signal the noise is distributed over the IMFs, the Rao-Blackwellised particle filtering (RBPF) is used to track the actual instantaneous phase from the noisy IMF. The formulated RBPF operates based on smoothing the instantaneous frequency traces in Hilbert domain and denoising the signal in time domain. Finally, the method is able to track the instantaneous phases across consecutive time points. The method is applied to both simulated and real data. As an application, it can be used for mental fatigue analysis based on the changes in phase synchronization of different brain rhythms in different brain regions before and during the fatigue state.