Overview
- Concise yet thorough overview provides self-contained introduction to theory
- Covers a broad range of state-of-the-art applications in many disciplines, including medical imaging and radar processing
- Abundant problems, exercises, and projects reinforce integration of theory with applications
- Useful for both undergraduates and graduates in mathematics and engineering-related sciences
- Adaptable to one and two semester courses and independent study
- Includes supplementary material: sn.pub/extras
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study.
Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medi
cal imaging, and heat and wave equations. For all applications, ample practice exercises are given throughout, with collections of more in-depth problems built up into exploratory chapter projects.  Illuminating videos are available on Springer.com and Link.Springer.com that present animated visualizations of several concepts.The content of the book itself is limited to what students will need to deal with in these fields, and avoids spending undue time studying proofs or building toward more abstract concepts. The book is perhaps best suited for courses aimed at upper division undergraduates and early graduates in mathematics, electrical engineering, mechanical engineering, computer science, physics, and other natural sciences, but in general it is a highly valuable resource for introducing a broad range of students to Fourier analysis.
Authors and Affiliations
About the author
He is also an experienced fly-fisherman and a fishing guide in the rivers of Montana.
Bibliographic Information
Book Title: Applied Fourier Analysis
Book Subtitle: From Signal Processing to Medical Imaging
Authors: Tim Olson
DOI: https://doi.org/10.1007/978-1-4939-7393-4
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2017
Hardcover ISBN: 978-1-4939-7391-0
Softcover ISBN: 978-1-4939-8471-8
eBook ISBN: 978-1-4939-7393-4
Edition Number: 1
Number of Pages: XVI, 302
Number of Illustrations: 8 b/w illustrations, 118 illustrations in colour
Topics: Fourier Analysis, Signal, Image and Speech Processing, Partial Differential Equations, Applications of Mathematics