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

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'.