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A First Course on Wavelets.
・ISBN 978-0-8493-8274-1 hard GB£ 210.00
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| 著者・編者 | Hernandez, Eugenio / Weiss, Guido, |
|---|---|
| シリーズ | (Studies in Advanced Mathematics) |
| 出版社 | (CRC Press Inc, US) |
| 出版年月 | 1996 |
| ページ数 | 512 pp. |
| 言語 | ENG |
| ニュース番号 | ＜A00-36781＞ |
解説
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:
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.