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

by Claude Gasquet (Author), Robert D. Ryan (Author), Patrick Witomski (Translator) "The purpose of signal theory is to study signals and the systems that transmit them..." (more)
Key Phrases: convolution system, generalized filter, periodic convolution, Exercises Exercise, Proposition Let, Definition Let (more...)

Editorial Reviews

Review
From the reviews: 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 Description
In all areas of modelling and numerical simulation scientists and engineers are faced with problems that require a collection of mathematical tools ranging from the classical - the Fourier transform, convolution, distributions - to the more recent wavelet-based techniques.

For this reason, the object of this text, which focuses on Fourier analysis, signal analysis and filters, is two-fold. On the one hand it conveys to the mathematician a rigorous presentation illustrated with important practical applications of the theory, including a discussion of Fast Fourier Transform. On the other hand it imparts to the physicist and engineer a body of theory in which the `well-known' formulae find their justification.

There is a systematic development of fundamental concepts, such as the Lebesgue integration and theory of distribution, that allows one to establish precise relations among several domains: Fourier transform and convolution; filtering and sampling; time-frequency analysis (gabor transforms and wavelets).

Each of the 42 lectures provides an easily assimilated set of ideas and techniques, suitable for both classroom or self-study. Maneuvering through the book is facilitated by grouping the lectures into 12 chapters and by adding numerous summary tables. This latter feature makes the book a handy reference for the subjects covered.

Senior undergraduate and graduate students in engineering, physics and mathematics will find this book helpful. It will also serve as a useful reference for scientists and engineers who deal with modelling and signal processing.

Product Details

• Hardcover: 464 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.com Sales Rank: #1,530,186 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

6 of 6 people found the following review helpful:

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

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

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.