The continuous wavelet transform : moving beyond uni and bivariate analysis

Abstract

A body of work using the continuous wavelet transform has been growing. We provide a self- contained summary on its most relevant theoretical results, describe how such transforms can be implemented in practice, and generalize the concept of simple coherency to partial wavelet coherency and multiple wavelet coherency, moving beyond bivariate analysis. We also describe a new family of wavelets, the generalized Morse wavelets, which have some desirable properties. A user-friendly toolbox, with examples, is attached to this paper.