Fast Fourier Transform - Algorithms and Applications

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.

• Preface. Acknowledgements. Acronyms. 1 Introduction. 2 Discrete Fourier Transform. 3 Fast Algorithms. 4 Integer Fast Fourier Transform. 5 Two-Dimensional Discrete Fourier Transform. 6 Vector-Radix 2-D FFT Algorithm. 7 Nonuniform DFT. 8 Applications. Appendix A: Performance Comparison of Various Discrete Transforms. Appendix B: Spectral Distance Measures of Image Quality. Appendix C: Integer Discrete Cosine Transform. Appendix D: DCT and DST. Appendix E: Kronecker Products and Separability. Appendix F: Mathematical Relations. Appendix G: Basics of MATLAB. Appendix H. Bibliography. Index.

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)