A wavelet-based method for local phase extraction from a multi-frequency oscillatory signal

One of the challenges in analyzing neuronal activity is to correlate discrete signal, such as action potentials with a signal having a continuous waveform such as oscillating local field potentials (LFPs). Studies in several systems have shown that some aspects of information coding involve characteristics that intertwine both signals. An action potential is a fast transitory phenomenon that occurs at high frequencies whereas a LFP is a low frequency phenomenon. The study of correlations between these signals requires a good estimation of both instantaneous phase and instantaneous frequency. To extract the instantaneous phase, common techniques rely on the Hilbert transform performed on a filtered signal, which discards temporal information. Therefore, time-frequency methods are best fitted for non-stationary signals, since they preserve both time and frequency information. We propose a new algorithmic procedure that uses wavelet transform and ridge extraction for signals that contain one or more oscillatory frequencies and whose oscillatory frequencies may shift as a function of time. This procedure provides estimates of phase, frequency and temporal features. It can be automated, produces manageable amounts of data and allows human supervision. Because of such advantages, this method is particularly suitable for analyzing synchronization between LFPs and unitary events.