A Complete Introduction to Fourier Analysis and its Applications

 A bridge between the rigorous foundations and the many rich applications of Fourier Analysis.

Applied Fourier Analysis

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

A Bridge Between Disciplines

Applied Fourier Analysis was created to bridge the gap between mathematics, engineering, physics, and computer science and other sciences.

This course will allow students from Mathematics, Physics, Engineering and elsewhere to gain some mathematical rigor in Fourier Analysis, as well as understand some of the many rich applications of Fourier Analysis.

Three Mathematical Building Blocks

The book is built around three fundamental chapters:  Fourier Series, The Discrete Fourier Transform, and The Continuous Fourier Transform.  The interplay between these three approaches is emphasized throughout.  The basic concepts of Convolution, The Fourier Isometry, Differentiation and Decay rates are compared between chapters.  The Uncertainty Principle and the other basic Fourier Identities are intertwined to give a great base for applications.

The Applications

Applications include:  Sampling and Interpolation, Medical Imaging, Image Processing, Radar Imaging, PDE's, and Digital Communications.  There are numerous videos throughout the book, available through both hard and electronic copies, which illustrate all of the theory and concepts.

A concise intro to a Varied Subject

Accessible

 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 imaging, and heat and wave equations. 

Applications, examples, and exercises

 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. 

A great intro to a vast subject

 The content of the book itself is limited to what students will need to begin to understand the wide variety within these various academic fields. The approach avoids spending undue time studying proofs or building toward more abstract concepts.  

The intended audience

 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. It can also be a highly valuable resource for introducing a broad range of students to Fourier analysis, or for self-study. 

Various Media

Choose your favorite form of media for this book.

  • Hard Copy
  • Electronic Copy

Both give access to embedded videos

Table of Contents

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