A new Framework for the Spectral Information Decomposition of Multivariate Gaussian Processes

: Different information-theoretic measures are available in the literature for the study of pairwise and higher-order interactions in multivariate dynamical systems. While these measures operate in the time domain, several physiological and non-physiological systems exhibit a rich oscillatory content that is typically analyzed in the frequency domain through spectral and cross-spectral approaches. For Gaussian systems, the relation between information and spectral measures has been established considering coupling and causality measures, but not for higher-order interactions. To fill this gap, in this work we introduce an information-theoretic framework in the frequency domain to quantify the information shared between a target process and two sources, even multivariate, and to highlight the presence of redundancy and synergy in the analyzed dynamical system. Firstly, we simulate different linear interacting processes by showing the capability of the proposed framework to retrieve amounts of information shared by the processes in specific frequency bands which are not detectable by the related time-domain measures. Then, the framework is applied on EEG time series representative of the brain activity during a motor execution task in a group of healthy subjects.