Applied Fourier Analysis

From Signal Processing to Medical Imaging

  • Tim Olson

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Tim Olson
    Pages 19-73
  3. Tim Olson
    Pages 75-120
  4. Tim Olson
    Pages 121-148
  5. Tim Olson
    Pages 149-176
  6. Tim Olson
    Pages 177-203
  7. Tim Olson
    Pages 205-226
  8. Tim Olson
    Pages 227-253
  9. Tim Olson
    Pages 255-277
  10. Tim Olson
    Pages 279-297
  11. Back Matter
    Pages 299-302

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, medical i

maging, 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.   

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.


Fourier applications analysis communications medical imaging sampling

Authors and affiliations

  • Tim Olson
    • 1
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

Bibliographic information