An Introduction to Wavelet Analysis

Rating:
Summary: From Fourier to wavelets to applications.
Review: I take it as a healthy sign when there is a burst of new books in a sub-area of math. In wavelet analysis and its applications, we have seen a number of recent books arrive to university bookstores. Surprisingly there doesn't in fact seem to be much of an overlap of subject or scope, from one book to the next. The subject is infinite in many directions, for example the kind of student it is aimed at, the level, the specialized area within math itself, and the kind of application it is stressing. D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material, for example Fourier series, than is typically the case in a graduate text. It goes from Haar systems to multirelutions, and then the discrete wavelet transform, starting on page 215. The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes.-- Highly recommended!