A First Course on Wavelets (Studies in Advanced Mathematics)

Hernandez, Eugenio; Weiss, Guido

ISBN 10: 0849382742 / ISBN 13: 9780849382741

Published by CRC Press, Boca Raton, 1996

About this Item

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Seller Inventory # 00043639

Bibliographic Details

• Title: A First Course on Wavelets (Studies in Advanced Mathematics)
• Publisher: CRC Press, Boca Raton
• Publication Date: 1996
• Language: English
• ISBN 10: 0849382742
• ISBN 13: 9780849382741
• Binding: Hardcover
• Edition: First Edition
• Condition: Very Fine
• Seller catalogs:
  • Computer Studies & Technology

About this title

Synopsis

Wavelet theory had its origin in quantum field theory, signal analysis, and function space theory. In these areas wavelet-like algorithms replace the classical Fourier-type expansion of a function. This unique new book is an excellent introduction to the basic properties of wavelets, from background math to powerful applications. The authors provide elementary methods for constructing wavelets, and illustrate several new classes of wavelets.

The text begins with a description of local sine and cosine bases that have been shown to be very effective in applications. Very little mathematical background is needed to follow this material. A complete treatment of band-limited wavelets follows. These are characterized by some elementary equations, allowing the authors to introduce many new wavelets. Next, the idea of multiresolution analysis (MRA) is developed, and the authors include simplified presentations of previous studies, particularly for compactly supported wavelets.

Some of the topics treated include:

Several bases generated by a single function via translations and dilations

Multiresolution analysis, compactly supported wavelets, and spline wavelets

Band-limited wavelets

Unconditionality of wavelet bases

Characterizations of many of the principal objects in the theory of wavelets, such as low-pass filters and scaling functions

The authors also present the basic philosophy that all orthonormal wavelets are completely characterized by two simple equations, and that most properties and constructions of wavelets can be developed using these two equations. Material related to applications is provided, and constructions of splines wavelets are presented.

Mathematicians, engineers, physicists, and anyone with a mathematical background will find this to be an important text for furthering their studies on wavelets.

About the Author

Eugenio Hernandez