Mathematics of the Discrete Fourier Transform (DFT)

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About the author:
Julius O. Smith is a research engineer and musician devoted to developing new technologies for music. He received the B.S.E.E. degree from Rice University, Houston, TX, in 1975 (Control, Circuits, and Communication). He received the M.S. and Ph.D. degrees in E.E. from Stanford University, Stanford, CA, in 1978 and 1983, respectively. His Ph.D. research was devoted to improved methods for digital filter design and system identification applied to music and audio systems. From 1975 to 1977 he worked in the Signal Processing Department at ESL, Sunnyvale, CA, on systems for digital communications. From 1982 to 1986 he was with the Adaptive Systems Department at Systems Control Technology, Palo Alto, CA, where he worked in the areas of adaptive filtering and spectral estimation. From 1986 to 1991 he was employed at NeXT Computer, Inc., responsible for sound, music, and signal processing software for the NeXT computer workstation. After NeXT, he became an Associate Professor at the Center for Computer Research in Music and Acoustics (CCRMA) at Stanford, teaching courses and pursuing research related to signal processing techniques applied to music and audio systems. Continuing this work, he is presently a Professor of Music and Associate Professor of Electrical Engineering (by courtesy) at Stanford University. For more information, see

Mathematics of the Discrete Fourier Transform (DFT)

with Audio Applications ---- Second Edition

Authored by Julius O. Smith III

Detailed derivation of the Discrete Fourier Transform (DFT) and its associated mathematics, including elementary audio signal processing applications and matlab programming examples.

Publication Date:
097456074X / 9780974560748
Page Count:
Binding Type:
US Trade Paper
Trim Size:
6" x 9"
Black and White
Related Categories:
Education / Computers & Technology

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