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International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 20682, 3 pages
http://dx.doi.org/10.1155/2007/20682
Research Article

Logarithm of the Discrete Fourier Transform

Digipen Institute of Technology, Redmond, WA 98052, USA

Received 1 June 2007; Accepted 7 August 2007

Academic Editor: Jonathan M. Borwein

Copyright © 2007 Michael Aristidou and Jason Hanson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The discrete Fourier transform defines a unitary matrix operator. The logarithm of this operator is computed, along with the projection maps onto its eigenspaces. A geometric interpretation of the discrete Fourier transform is also given.