Time-varying spectral analysis in neurophysiological time series using Hilbert wavelet pairs

An analytic wavelet transform, based on Hilbert wavelet pairs, is applied to bivariate time-varying spectral estimation for neurophysiological time series. Under the assumption of an underlying block stationary process, both single-trial and ensemble studies are amenable to this method. A bootstrap procedure, which samples with replacement blocks centered around the events of interest, is proposed to identify time points for which the event-averaged magnitude squared coherence is non-zero. Clinical data sets are used to compare the wavelet-based technique with the classical Fourier-based spectral measures and highlight its ability to detect time-varying coherence and phase properties.