The principal results of this paper are listed as follows. 1) The eigenvalues of a suitably normalized version of the discrete Fourier transform (DFT) are <img src="/images/tex/14891.gif" alt="1, -1,j, -j"> . 2) An eigenvector basis is constructed for the DFT. 3) The multiplicities of the eigenvalues are summarized for an N×N transform as follows.
%0 Journal Article
%1 mcclellan72
%A McClellan, James H.
%A Parks, Thomas W.
%D 1972
%J Audio and Electroacoustics, IEEE Transactions on
%K chebyshev.set circulant dft eigenvalues fourier haar linear.algebra matrix
%N 1
%P 66--74
%R 10.1109/TAU.1972.1162342
%T Eigenvalue and Eigenvector Decomposition of the Discrete Fourier Transform
%V 20
%X The principal results of this paper are listed as follows. 1) The eigenvalues of a suitably normalized version of the discrete Fourier transform (DFT) are <img src="/images/tex/14891.gif" alt="1, -1,j, -j"> . 2) An eigenvector basis is constructed for the DFT. 3) The multiplicities of the eigenvalues are summarized for an N×N transform as follows.
@article{mcclellan72,
abstract = {The principal results of this paper are listed as follows. 1) The eigenvalues of a suitably normalized version of the discrete Fourier transform (DFT) are <img src="/images/tex/14891.gif" alt="{1, -1,j, -j}"> . 2) An eigenvector basis is constructed for the DFT. 3) The multiplicities of the eigenvalues are summarized for an N×N transform as follows.},
added-at = {2015-09-03T04:26:52.000+0200},
author = {McClellan, James H. and Parks, Thomas W.},
biburl = {https://www.bibsonomy.org/bibtex/237070fd9b1082075b73f0ce6761873c5/ytyoun},
doi = {10.1109/TAU.1972.1162342},
interhash = {f629dfdd5ac0bd2162583b77a75698b7},
intrahash = {37070fd9b1082075b73f0ce6761873c5},
issn = {0018-9278},
journal = {Audio and Electroacoustics, IEEE Transactions on},
keywords = {chebyshev.set circulant dft eigenvalues fourier haar linear.algebra matrix},
month = mar,
number = 1,
pages = {66--74},
timestamp = {2015-12-21T09:40:13.000+0100},
title = {Eigenvalue and Eigenvector Decomposition of the Discrete {Fourier} Transform},
volume = 20,
year = 1972
}