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Acknowledgments

Thanks to my graduate students and research colleagues Sean Bratnober, Mark Cartwright, Humane Chan, Rob Hamilton, Miriam Kolar, Randal Leistikow, Sandy Lin, Gautham Mysore, Juhan Nam, Jeonghun Noh, Brook Reeder, Bill Schottstaedt, Sook Young Won, Vivian Woo, and Matt Wright for helpful errata reporting and other suggestions based on earlier precursors to this book. Special thanks are due to Miller Puckette for some especially useful contributions. Thanks also to netizens Greg Allen, Adi Biton, John Brenneise, David Holman, Alexander Kraus, Nima Maftoon, Niels Moseley, Hirak Parikh, and Eric Woudenberg for reporting errata in the draft versions on the Web. Additionally, email discussions with Steven Johnson (co-author of the well known FFTW software package) contributed greatly to the appendix on FFT algorithms.

Many thanks to my 1997 teaching assistant Craig Stuart Sapp for writing the Mathematica magic for Figures 4.9 (adapted for the cover), 4.17, 4.18, 4.19, 7.5, 7.9, 7.11, and 7.12.

Thanks also to Prof. C. Sidney Burrus of Rice University for teaching me and others the fundamentals of digital signal processing, including the DFT.

Finally, thanks to my wife Carol for her encouragement and support, and for putting up with all those ``working Saturdays'', and to my son Harrison, age 9, for his many inspirations, both musical and mathematical, among others.



Julius Smith
April, 2007


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``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8.
Copyright © 2014-04-06 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA