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This book provides a systematic exposition of the basic ideas and
results of wavelet analysis suitable for mathematicians,
scientists, and engineers alike. The primary goal of this text is
to show how different types of wavelets can be constructed,
illustrate why they are such powerful tools in mathematical
analysis, and demonstrate their use in applications. It also
develops the required analytical knowledge and skills on the part
of the reader, rather than focus on the importance of more abstract
formulation with full mathematical rigor. These notes differs from
many textbooks with similar titles in that a major emphasis is
placed on the thorough development of the underlying theory before
introducing applications and modern topics such as fractional
Fourier transforms, windowed canonical transforms, fractional
wavelet transforms, fast wavelet transforms, spline wavelets,
Daubechies wavelets, harmonic wavelets and non-uniform wavelets.
The selection, arrangement, and presentation of the material in
these lecture notes have carefully been made based on the authors'
teaching, research and professional experience. Drafts of these
lecture notes have been used successfully by the authors in their
own courses on wavelet transforms and their applications at the
University of Texas Pan-American and the University of Kashmir in
India.
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