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Changing Coordinates

What's more interesting is when we project a signal $ x$ onto a set of vectors other than the coordinate set. This can be viewed as a change of coordinates in $ {\bf C}^N$ . In the case of the DFT, the new vectors will be chosen to be sampled complex sinusoids.



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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 © 2014-04-21 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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