Journal of Neuroscience Methods 111 (2001) 83 – 98 Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony Michel Le Van Quyen *, Jack Foucher, Jean-Philippe Lachaux, Eugenio Rodriguez, Antoine Lutz, Jacques Martinerie, Francisco J. Varela 1 Laboratoire de Neurosciences Cognities et Imagerie Ce ´re ´brale (LENA), Ho ˆpital de La Salpe ˆtrie `re, CNRS UPR 640, 47 Bd. de l’Ho ˆpital, 75651 Paris Cedex 13, France Received 29 March 2001; received in revised form 24 April 2001; accepted 25 April 2001 Abstract The quantification of phase synchrony between neuronal signals is of crucial importance for the study of large-scale interactions in the brain. Two methods have been used to date in neuroscience, based on two distinct approaches which permit a direct estimation of the instantaneous phase of a signal [Phys. Rev. Lett. 81 (1998) 3291; Human Brain Mapping 8 (1999) 194]. The phase is either estimated by using the analytic concept of Hilbert transform or, alternatively, by convolution with a complex wavelet. In both methods the stability of the instantaneous phase over a window of time requires quantification by means of various statistical dependence parameters (standard deviation, Shannon entropy or mutual information). The purpose of this paper is to conduct a direct comparison between these two methods on three signal sets: (1) neural models; (2) intracranial signals from epileptic patients; and (3) scalp EEG recordings. Levels of synchrony that can be considered 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 neuroelectrical signals. This offers a common language and framework that can be used for future research in the area of synchronization. © 2001 Published by Elsevier Science B.V. Keywords: Phase synchrony; Neural synchrony; Hilbert transform; Wavelet transform; Surrogate data www.elsevier.com/locate/jneumeth 1. Introduction 1.1. A brief background on neural synchrony Synchronization on various levels of organization of brain tissue, from individual pairs of neurons to much larger scales, within one area of the brain or between different parts of the brain, is one of the most active topics in current neuroscience. In particular normal cognitive operations require the transient integration of numerous functional areas widely distributed over the brain and in constant interaction with each other (Damasio, 1990; Varela, 1995; Friston, 1997; Tononi and Edelman, 1998; Varela et al., 2001). Neural syn- chrony is an important candidate for such large-scale integration, mediated by neuronal groups that oscillate in specific bands and enter into precise phase-locking over a limited period of time. This has, in turn, moti- vated the search for robust methods for directly mea- suring such phase-synchrony in this frequency band from experimentally recorded biological signals. The role of synchronization of neuronal discharges, although not a new idea, has been greatly highlighted by results from microelectrodes in animals (see, e.g. Singer and Gray, 1995; Roelfsema et al., 1997; Neuron, 1999). These single-unit recording studies in animals have been complemented by studies at coarser levels of resolution in humans and animals (Freeman, 1978). These are not spikes, but local field potentials (LFP) of various degrees of spatial resolution, including scalp recording in EEG or MEG. In fact, gamma and beta band responses can be recorded during visual discrimi- nation protocols on the human scalp (Tallon-Baudry et al., 1997) and in subdural electrocorticograms (Le Van * Corresponding author. Tel.: +331-42-16-1166. E-mail address: lenalm@ext.jussieu.fr (M. Le Van Quyen). 1 Deceased. 0165-0270/01/$ - see front matter © 2001 Published by Elsevier Science B.V. PII:S0165-0270(01)00372-7