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Book review

Author(s) Young, R.K.
Title Wavelet theory and its applications
Publisher Kluwer Academic Publishers
Year of publication 1993
Reviewed by Anatoly Zhigljavsky

Several good books devoted to the wavelet theory have recently appeared. Among them are I. Daubechies, Ten lectures on wavelets, SIAM, 1992; C.K. Chui, An introduction to wavelets, Academic Press, 1992; Meyer Y., Wavelets: algorithms and applications, SIAM, 1993; T.H. Koornwinder (ed.), Wavelets: an elementary treatment of theory and applications, World Scientific, 1993.

The present monograph is mainly addressed to those interested in some particular applications of the wavelet theory in signal processing. The book starts with a short pictorial introduction to some ideas of the classical wavelet theory and then only a specific approach of the wavelet transform methodology is considered. This approach is based on consideration of operators mapping a wavelet transform with respect to one mother wavelet to a new wavelet transform with respect to another mother wavelet and on continuous wavelet transforms of the wavelets that are not necessarily orthogonal. Some properties of these wavelet transforms and of some characteristics of closeness of different wavelet transforms are established. Also several examples from the signal processing field are considered.

The book contains a lot of illustrative material and might be understood even by the readers that are not professional mathematicians. Furthermore, the book is not an easy reading for mathematicians since it does not contain strong mathematical statements and the style is a bit discursive. It looks like the author is relatively young and did not get a strong mathematical background. Therefore the book can only be recommended for the engineers, specialists in signal processing, looking for new mathematical tools in their research. The mathematicians specializing in the theory of wavelets may also find some ideas of the book to be of interest for them.

The book is not cheap and I do not think I should advise to mathematicians to buy it. Specialists in signal processing may find it more attractive. Perhaps it is worthwhile to purchase the book for the libraries of the institutions having the wavelet theory and/or the signal processing in their activity.