%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&#215;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&#215;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 }