Applied Fourier Analysis: From Signal Processing to Medical Imaging

✍ Scribed by Tim Olson (auth.)

• Publisher: Birkhäuser Basel
• Year: 2017
• Tongue: English
• Leaves: 310
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xvi
Introduction: From Linear Algebra to Linear Analysis (Tim Olson)....Pages 1-17
Basic Fourier Series (Tim Olson)....Pages 19-73
The Discrete Fourier Transform (Tim Olson)....Pages 75-120
The Fourier Transform (Tim Olson)....Pages 121-148
Sampling and Interpolation (Tim Olson)....Pages 149-176
Digital Communications (Tim Olson)....Pages 177-203
Radar Processing (Tim Olson)....Pages 205-226
Image Processing (Tim Olson)....Pages 227-253
Medical Imaging (Tim Olson)....Pages 255-277
Partial Differential Equations (Tim Olson)....Pages 279-297
Back Matter ....Pages 299-302

✦ Subjects

Fourier Analysis