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Eigenvalue and eigenvector decomposition of the discrete Fourier transform

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2 Author(s)
McClellan, J.H. ; Rice University, Houston, TX ; Parks, T.W.

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{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.

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Audio and Electroacoustics, IEEE Transactions on  (Volume:20 ,  Issue: 1 )