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Engineering LibreTexts

Fast Fourier Transforms (Burrus)

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  • 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. This book uses an index map, a polynomial decomposition, an operator factorization, and a conversion to a filter to develop a very general and efficient description of fast algorithms to calculate the discrete Fourier transform (DFT). The work of Winograd is outlined, chapters by Selesnick, Pueschel, and Johnson are included, and computer programs are provided.

    Thumbnail: Animation showing a Fourier series approximating a sawtooth wave. (CC BY-SA 3.0 Unported; 4dhayman via Wikipedia)

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