Multivariate scale-free temporal dynamics: From spectral (Fourier) to fractal (wavelet) analysis

Publication date: Available online 20 September 2019Source: Comptes Rendus PhysiqueAuthor(s): Patrice Abry, Herwig Wendt, Stéphane Jaffard, Gustavo DidierAbstractThe Fourier transform (or spectral analysis) has become a universal tool for data analysis in many different real-world applications, notably for the characterization of temporal/spatial dynamics in data. The wavelet transform (or multiscale analysis) can be regarded as tailoring spectral estimation to classes of signals or functions defined by scale-free dynamics. The present contribution first formally reviews these connections in the context of multivariate stationary processes, and second details the ability of the wavelet transform to extend multivariate scale-free temporal dynamics analysis beyond second-order statistics (Fourier spectrum and autocovariance function) to multivariate self-similarity and multivariate multifractality. Illustrations and qualitative discussions of the relevance of scale-free dynamics for macroscopic brain activity description using MEG data are proposed.RésuméLa transformée de Fourier (ou analyse spectrale) est aujourd'hui devenue un outil universel pour l'analyse de données issues de nombreuses applications réelles de natures très différentes, particulièrement pertinent pour la caractérisation de la dynamique temporelle ou spatiale. La transformée en ondelettes (ou analyse multéchelle) peut être vue comme une analyse spectrale adaptée à des classes de signaux ou fonc...

Source: Comptes Rendus Physique - September 21, 2019 Category: Physics Source Type: research