Here are selected references to the wavelet literature and brief commentary. Although some papers belong in the `turbulence’ literature, I included them because they deal with a broader point. This list is not about field- (e.g. turbulence) or topic-specific (e.g. structure functions) results.
I Daubechies, 10 Lectures on
Wavelets,
Continuous wavelets get a good treatment here, as do
non-orthogonal discrete wavelets (theory of frames). I prefer some later
presentations of multiresolution analysis.
Wavelab website http://www-stat.stanford.edu/~wavelab
Thanks to D. Donoho and coworkers for this wonderful resource with Matlab library!
M Farge & K. Schneider, Physics of Fluids 11(8), 2187-2201 (1999)
Applications to turbulence aside, the idea that structures are multiscale events in the orthogonal representation should get more attention. The concept of scale-dependent structure needs to be justified more carefully in papers by other authors. See http://wavelets.ens.fr for related papers.
M Germano, Journal of Fluid Mechanics 238, 325-336 (1992)
Iterative filtering and the implicit use of filters to discretize continuous fields should be of interest outside the turbulence community.
J Harrop’s web site http://www.ffconsultancy.com
Mathematica software can be obtained here
Very clear and thorough, Matlab codes are reproduced in Wavelab
DF Walnut, An Introduction to Wavelet Analysis, Birkhauser (2002)
A bit harder than Mallat’s for the non-mathematician, different content
selection including `best wavelets’.
There are many others!