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Derivation of the Discrete Fourier Transform (DFT)

This chapter derives the Discrete Fourier Transform (DFT) as a projection of a length $ N$ signal $ x$ onto the set of $ N$ sampled complex sinusoids generated by the $ N$th roots of unity.



Subsections
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[How to cite this work] [Order a printed hardcopy]

``Mathematics of the Discrete Fourier Transform (DFT), with Music and Audio Applications'', by Julius O. Smith III, W3K Publishing, 2003, ISBN 0-9745607-0-7.
Copyright © 2007-02-02 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA  [Automatic-links disclaimer]