Fast Fourier Transforms

This book focuses on the discrete Fourier transform (DFT), discrete convolution, and, particularly, the fast algorithms to calculate them.

**Tag(s):**
Signal Processing

**Publication date**: 18 Nov 2012

**ISBN-10**:
n/a

**ISBN-13**:
9781300461647

**Paperback**:
254 pages

**Views**: 18,032

**Type**: Book

**Publisher**:
Connexions

**License**:
Creative Commons Attribution 3.0 Unported

**Post time**: 09 Aug 2017 12:00:00

Fast Fourier Transforms

This book focuses on the discrete Fourier transform (DFT), discrete convolution, and, particularly, the fast algorithms to calculate them.

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From the Preface:

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Burrus, et al. wrote:This book focuses on the discrete Fourier transform (DFT), discrete convolution, and, particularly, the fast algorithms to calculate them. These topics have been at the center of digital signal processing since its beginning, and new results in hardware, theory and applications continue to keep them important and exciting.

Burrus, et al. wrote:It is hard to overemphasis the importance of the DFT, convolution, and fast algorithms. With a history that goes back to Gauss [174] and a compilation of references on these topics that in 1995 resulted in over 2400 entries [362], the FFT may be the most important numerical algorithm in science, engineering, and applied mathematics. New theoretical results still are appearing, advances in computers and hardware continually restate the basic questions, and new applications open new areas for research. It is hoped that this book will provide the background, references, programs and incentive to encourage further research and results in this area as well as provide tools for practical applications.

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About The Editor(s)

Charles Sidney Burrus (born October 9, 1934 in Abilene, Texas) is an American electrical engineer and the Maxfield and Oshman Professor Emeritus of Electrical and Computer Engineering at Rice University in Houston, Texas. He is widely known for his contributions to digital signal processing, especially FFT algorithms, IIR filter design, and wavelets. In addition to DSP research, Dr. Burrus has been interested in the use of technology to teach and facilitate learning. He and five colleagues at other universities have published a book of exercises using Matlab (from MathWorks) to teach DSP. He has been part of the Connexions Project since its founding in 1999 and is now its Senior Strategist.

About The Author(s)

Matteo Frigo is an Italian computer scientist and programmer. Matteo received his Ph.D. in 1999 from the Department of Electrical Engineering and Computer Science at Massachusetts Institute of Technology. His dissertation received the 1999 George M. Sprowls award for outstanding doctoral dissertations in computer science at MIT. After architecting the Amazon Web Services (AWS) Elastic File System, Dr. Frigo is currently an Oracle software architect applying his deep knowledge and experience—and building a team of Boston-area technologists—to create a data center network that makes the Oracle cloud infrastructure service unique.

Steven G. Johnson is Professor of Applied Mathematics and Physics at Massachusetts Institute of Technology. He received his Ph.D. in physics from MIT in 2001, where he was also an undergraduate student (receiving B.S. degrees in physics, mathematics, and EECS in 1995). He joined the MIT faculty in applied mathematics in 2004, and was awarded tenure in 2011. He works on the influence of complex geometries (particularly in the nanoscale) on the solutions of partial differential equations, especially for wave phenomena and electromagnetism. He is also known for his work in high-performance computing, such as his development of the FFTW fast Fourier transform library (for which he received the 1999 J. H. Wilkinson Prize for Numerical Software).

Markus Püschel is a Professor of Computer Science at ETH Zurich, Switzerland, where he was the head of the department from 2013 to 2016. Before joining ETH in 2010, he was a Professor of Electrical and Computer Engineering at Carnegie Mellon University (CMU), where he still has an adjunct status. In 2009 he cofounded Spiralgen Inc. His research interests include program synthesis with the goal of high performance, fast computing, algorithms, applied mathematics, and signal processing theory/software/hardware.

Ivan Selesnick is a Professor in the Electrical and Computer Engineering Department of NYU Tandon School of Engineering. His research interests are in digital signal processing, sparsity in signal processing, and wavelet-based signal/image/video processing. His recent research focuses on using sparse signal representations and approximations to develop new methods for filtering, signal separation, deconvolution, etc. He has also recently worked on the design, implementation, and applications of new oriented multi-dimensional wavelet transforms; and on the development of non-Gaussian probability models for statistical signal processing.

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