Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets (Texts in Applied Mathematics) [Hardcover]

Claude Gasquet (Author), Robert D. Ryan (Author), Patrick Witomski (Author)

Book Description

ISBN-10: 0387984852 | ISBN-13: 978-0387984858 | Publication Date: November 6, 1998 | Edition: 1

The object of this book is two-fold -- on the one hand it conveys to mathematical readers a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations. On the other hand, it presents physics readers with a body of theory in which the well-known formulae find their justification. The basic study of fundamental notions, such as Lebesgue integration and theory of distribution, allow the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis time-frequency analysis (gabor transforms and wavelets). The whole is rounded off with a large number of exercises as well as selected worked-out solutions.

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BULLETIN OF MATHEMATICS BOOKS

"This book should have wide appeal, from those who are just getting into the area and wish to learn mathematical foundations and applications to those who are already experienced and wish to have a reference that provides a mathematically rigorous coverage of the state of the art…The coverage is thorough but not overwhelming, perhaps because the chapters are divided into lessons, allowing the reader a chance to pause and think. The authors work clearly to impart an understanding of the theory and applications, and not just offer an encyclopedic tome."

Product Details

• Hardcover: 482 pages
• Publisher: Springer; 1 edition (November 6, 1998)
• Language: English
• ISBN-10: 0387984852
• ISBN-13: 978-0387984858
• Product Dimensions: 9.3 x 6.5 x 1.3 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #630,006 in Books (See Top 100 in Books)

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7 of 7 people found the following review helpful:

5.0 out of 5 stars An excellent text for Fourier Analysis, May 22, 2002

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Todd Ebert (Long Beach California) - See all my reviews

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This review is from: Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets (Texts in Applied Mathematics) (Hardcover)

I bought this book hoping to find a self-contained, semi-rigorous introduction to Fourier Analysis and its applications, and indeed I'm very pleased with the purchase. One aspect of the book's format that I enjoyed in a self-study setting is how it is partitioned into lessons (which are in turn divided into chapters). Indeed, it seemed that each lesson took me about 60-90 minutes to absorb, which is the average time most students (including myself) devote to one lesson.

Another aspect of the book I enjoyed was the fact that, on one hand the author took the time to introduce mathematically sophisticated ideas such as Lesbesgue measure and Hilbert spaces in order to make the proofs run more smoothly, but on the other there where more practical lessons on the fast Fourier transform, filters, and even wavelet analysis (last lesson). Such a blend of theory and practice in a relatively compact text seems quite rare.

Finally, I highly recommend this book for students of all levels; but especially to graduate students in mathematics, physics, and engineering.