Interesting Eigenvectors of the Fourier Transform
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Author(s)
Horn, Berthold Klaus Paul
Date Issued
June 2010
Journal
Transactions of the Royal Society of South Africa
Publisher
Taylor & Francis
Citation
Horn, Berthold K.P. “Interesting Eigenvectors of the Fourier Transform.” Transactions of the Royal Society of South Africa 65.2 (2010) : 100-106.
Version
Author's final manuscript
Abstract
It is well known that a function can be decomposed uniquely into the sum of an odd and an even function. This notion can be extended to the unique decomposition into the sum of four functions – two of which are even and two odd. These four functions are eigenvectors of the Fourier Transform with four different eigenvalues. That is, the Fourier transformof each of the four components is simply that component multiplied by the corresponding eigenvalue. Some eigenvectors of the discrete Fourier transform of particular interest find application in coding, communication and imaging. Some of the underlying mathematics goes back to the times of Carl Friedrich Gauss.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1080/0035919X.2010.510665
