Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony

The quantification of phase synchrony between neuronal signals is of crucia l importance for the study of large-scale interactions in the brain. Two me thods have been used to date in neuroscience, based on two distinct approac hes which pen-nit a direct estimation of the instantaneous phase of a signa l [Phys. Rev. Lett. 81 (1998) 3291; Human Brain Mapping 8 (1999) 194]. The phase is either estimated by using the analytic concept of Hilbert transfor m or, alternatively, by convolution with a complex wavelet. In both methods the stability of the instantaneous phase over a window of time requires qu antification by means of various statistical dependence parameters (standar d deviation, Shannon entropy or mutual information). The purpose of this pa per is to conduct a direct comparison between these two methods on three si gnal sets: (1) neural models; (2) intracranial signals from epileptic patie nts; and (3) scalp EEG recordings. Levels of synchrony that can be consider ed as reliable are estimated by using the technique of surrogate data. Our results demonstrate that the differences between the methods are minor, and we conclude that they are fundamentally equivalent for the study of neuroe lectrical signals. This offers a common language and framework that can be used for future research in the area of synchronization. (C) 2001 Published by Elsevier Science B.V.