Introduction to redundancy rules: the continuous wavelet transform comes of age

Abstract

Redundancy: it is a word heavy with connotations of lacking usefulness. I often hear that the rationale for not using the continuous wavelet transform (CWT)—even when it appears most appropriate for the problem at hand—is that it is ‘redundant’. Sometimes the conversation ends there, as if self-explanatory. However, in the context of the CWT, ‘redundant’ is not a pejorative term, it simply refers to a less compact form used to represent the information within the signal. The benefit of this new form—the CWT—is that it allows for intricate structural characteristics of the signal information to be made manifest within the transform space, where it can be more amenable to study: resolution over redundancy. Once the signal information is in CWT form, a range of powerful analysis methods can then be employed for its extraction, interpretation and/or manipulation. This theme issue is intended to provide the reader with an overview of the current state of the art of CWT analysis methods from across a wide range of numerate disciplines, including fluid dynamics, structural mechanics, geophysics, medicine, astronomy and finance. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.