© 2015

Digital Fourier Analysis: Fundamentals

  • Covers the basic theory of the discrete and Fast Fourier transform and shows how they are implemented, using clear explanations and a large number of step-by-step illustrations

  • Interactive animated applets, freely available online, richly illustrate the book and allow the reader to explore the subject dynamically

  • Practice problems are included at the end of each chapter

  • A large number of Appendices provide more detailed derivations and explanations for the interested reader


Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ken’iti Kido
    Pages 1-24
  3. Ken’iti Kido
    Pages 25-50
  4. Ken’iti Kido
    Pages 51-75
  5. Ken’iti Kido
    Pages 77-105
  6. Ken’iti Kido
    Pages 107-130
  7. Ken’iti Kido
    Pages 131-151
  8. Ken’iti Kido
    Pages 153-181
  9. Back Matter
    Pages 183-203

About this book


This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform.

Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations.  These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics.

For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader can test various cases and view the results until they fully understand the principle.

Additionally, the applet source code in Visual Basic is provided online, allowing this book to be used for teaching simple programming techniques.

A complete, intuitive guide to the basics, "Digital Fourier Analysis - Fundamentals" is an essential reference for undergraduate students in science and engineering.


Discrete Fourier Transform Fast Fourier Transform Fourier Transform Learning Tools Fourier Transform in Visual Basic Numerical Methods in Visual Basic Sine and Cosine Components Spectrum Analysis

Authors and affiliations

  1. 1.Yokohama-shiJapan

About the authors

Professor Kido is an internationally recognized expert in acoustics and engineering. Currently a professor at the Chiba Institute of Technology, Prof. Kido previously served as the Chairman of ONTEK R&D Co. Ltd., and earlier as the Director of the Research Center for Applied Information Sciences at Tohoku University. Prof. Kido was elected as a fellow of the Acoustical Society of America in 1978. He has published eight books in Japanese over a span of forty years.

Bibliographic information

Industry Sectors
Energy, Utilities & Environment


“This first volume of a two-volume series explores, as the title implies, the fundamentals of digital Fourier analysis, including some advanced topics in the appendixes. … Kido (Chiba Institute of Technology, Japan) does an excellent job of balancing a verbal explanation of the topics with mathematical formulas and equations. This combination makes the book very readable. … Summing Up: Recommended. Upper-division undergraduates and graduate students.” (S. L. Sullivan, Choice, Vol. 52 (10), June, 2015)

“This short and to-the-point book comprises the following seven chapters, and is replete with marvelously clear and effective graphs and illustrations: ‘Sine and Cosine Waves’; ‘Fourier Series Expansion[s]’; ‘Digitized Waveforms’; ‘Discrete Fourier Transform (DFT)’; ‘Fast Fourier Transform’; ‘DFT and [Its] Spectrum’; and ‘Time Window[s].’ … I recommend this excellent undergraduate textbook highly.” (George Hacken, Computing Reviews, January, 2015)