Wavelets: Theoretical concepts and vibrations related applications

In this paper we provide a review of wavelet
analysis in the context of applications to vibrations problems.
First, we give an introduction to the important concepts and
mathematical properties of wavelets within the framework of
time–frequency analysis of signals. Next, wavelet analysis is
discussed as applied to relevant themes in vibrations, such as
time-varying spectra estimation, random field synthesis, system
identification, damage detection, and material characterization.
In view of the large number of related books and journal
articles published in recent decades, the list of selected references
in the paper is not meant to be exhaustive. Nevertheless,
the cited references aim to point out the salient features
of wavelet analysis, and to identify significant contributions in
each theme, with the goal of expediting additional research
and development efforts