This is a thorough introduction to most aspects of wavelets. It is an unaltered reprint of a 1994 book, but it is still reasonably up-to-date for the topics it covers. It is slanted towards continuous wavelet transforms and towards signal processing, and emphasizes concepts rather than techniques. The last third of the book treats applications to electromagnetic and acoustic waves; these applications are also conceptual, and are intended to outline how problems in these areas might be attacked, not to give solutions.
The book is intended to be “friendly” toward engineering and scientific readers by using the language of classical analysis rather than that of abstract spaces. It assumes a good knowledge of Fourier transforms and of signal processing, and it is less friendly if you are not familiar with these.
Overall there is little to complain about with this book; its weaknesses have to do with the things it omits. It is not a how-to book or a cookbook, and does not cover algorithms. It omits some of the most important applications of wavelets, such as image compression. It does not deal with any computational aspects of the subject, so (for example) there is no fast wavelet transform.
Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.org, a math help site that fosters inquiry learning.
Preface.- Suggestions to the Reader.- Symbols, Conventions, and Transforms.- Part I: Basic Wavelet Analysis. Preliminaries: Background and Notation.- Windowed Fourier Transforms.- Continuous Wavelet Transforms.- Generalized Frames: Key to Analysis and Synthesis.- Discrete Time-Frequency Analysis and Sampling.- Discrete Time-Scale Analysis.- Multiresolution Analysis.- Daubechies’ Orthonormal Wavelet Bases.- Part II: Physical Wavelets.- Introduction to Wavelet Electromagnetics.- Applications to Radar and Scattering.- Wavelet Acoustics.- References.- Index.