© 2010

Fast Fourier Transform - Algorithms and Applications


  • Specific applications in signal and image processing

  • Web/ftp sites, computer projects, Integer FFT, Basics of MATLAB, M-Files

  • Ridgelets, curvelets, nonuniform DFT


Part of the Signals and Communication Technology book series (SCT)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. K. R. Rao, D. N. Kim, J. J. Hwang
    Pages 1-3
  3. K. R. Rao, D. N. Kim, J. J. Hwang
    Pages 5-40
  4. K. R. Rao, D. N. Kim, J. J. Hwang
    Pages 41-110
  5. K. R. Rao, D. N. Kim, J. J. Hwang
    Pages 111-126
  6. K. R. Rao, D. N. Kim, J. J. Hwang
    Pages 127-184
  7. K. R. Rao, D. N. Kim, J. J. Hwang
    Pages 185-193
  8. K. R. Rao, D. N. Kim, J. J. Hwang
    Pages 195-234
  9. K. R. Rao, D. N. Kim, J. J. Hwang
    Pages 235-316
  10. Back Matter
    Pages 317-423

About this book


Fast Fourier Transform - Algorithms and Applications presents an introduction to the principles of the fast Fourier transform (FFT). It covers FFTs, frequency domain filtering, and applications to video and audio signal processing.

As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of the essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics.

Fast Fourier Transform - Algorithms and Applications provides a thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.

Fast Fourier Transform - Algorithms and Applications is designed for senior undergraduate and graduate students, faculty, engineers, and scientists in the field, and self-learners to understand FFTs and directly apply them to their fields, efficiently. It is designed to be both a text and a reference. Thus examples, projects and problems all tied with MATLAB, are provided for grasping the concepts concretely. It also includes references to books and review papers and lists of applications, hardware/software, and useful websites. By including many figures, tables, bock diagrams and graphs, this book helps the reader understand the concepts of fast algorithms readily and intuitively. It provides new MATLAB functions and MATLAB source codes. The material in Fast Fourier Transform - Algorithms and Applications is presented without assuming any prior knowledge of FFT. This book is for any professional who wants to have a basic understanding of the latest developments in and applications of FFT. It provides a good reference for any engineer planning to work in this field, either in basic implementation or in research and development.


Applications Discrete Fourier Transform Distribution Fast Algorithms Fourier transform Signal and image processing communication convolution fast Fourier transform fast Fourier transform (FFT)

Authors and affiliations

  1. 1.Electr. Engineering, Neddermann HallUniv. of Texas at ArlingtonArlingtonUSA
  2. 2.Electr. Engineering, Neddermann HallUniv. of Texas at ArlingtonArlingtonUSA
  3. 3.School of Electron.&Inform. EngineeringKunsan National Univ.KunsanKorea, Republic of (South Korea)

About the authors

Prof. K. R. Rao received the Ph. D. degree in electrical engineering from The University of New Mexico, Albuquerque in 1966. Since 1966, he has been with the University of Texas at Arlington where he is currently a professor of electrical engineering. He, along with two other researchers, introduced the Discrete Cosine Transform in 1975 which has since become very popular in digital signal processing. Some of his books have been translated into Japanese, Chinese, Korean and Russian. He has conducted workshops/tutorials on video/audio coding/standards worldwide. He has published extensively in refereed journals and has been a consultant to industry, research institutes and academia. He is a Fellow of the IEEE.

Bibliographic information

Industry Sectors
Finance, Business & Banking


From the reviews:

The new book Fast Fourier Transform - Algorithms and Applications by Dr. K.R. Rao, Dr. D.N. Kim, and Dr. J.J. Hwang is an engaging look in the world of FFT algorithms and applications. This book not only provides detailed description of a wide-variety of FFT algorithms, gives the mathematical derivations of these algorithms, plentiful helpful flow diagrams illustrating the algorithms, and MATLAB programsthe book also presents novel topics in depth (for example, integer FFTs, the non-uniform DFT, phase-only correlation, image and audio watermarking, the curvelet transform, and many more) with insightful motivation, explanation, and numerous examples and programs. The authors also provide insight into issues related to implementation of FFTs on different hardware platforms. Excellent aspects of the book are the plentiful numerical examples illustrating the properties of the DFT and a most impressive number of applications of the FFT- including applications in communications, image restoration, and descriptions of audio coding standards that rely on the FFT (MPEG, AC-2) to name only a few. The book also supplies a generous number of exercises and computer projects. In addition, throughout the book the authors present and discuss the research literature at length and include many healthy doses of pointers to the literature which provides a pathway for specialized further study.

Dr. Ivan W. Selesnick, Polytechnic University, New York, NY

“The fast Fourier transform (FFT) is an essential tool in applied mathematics and digital signal processing. … This monograph on the FFT is mainly written for graduate students and researchers in engineering and science. It consists of 8 chapters, 8 appendices and a comprehensive bibliography.” (Manfred Tasche, Zentralblatt MATH, Vol. 1203, 2011)

“This volume … offers an account of the Discrete Fourier Transform (DFT) and its implementation, including the Fast Fourier Transform (FFT). The target audience is clearly instructors and students in engineering … . book gives an excellent opportunity to applied mathematicians interested in refreshing their teaching to enrich their presentation of the DFT/FFT with modern applications. The exercises and projects … are one of the most important feature of this volume. This is in itself a clear motivation to strongly recommend this volume … .” (Jean-Pierre Croisille Mathematical Reviews, Issue 2012 k)