Eigenvalue and eigenvector decomposition of the discrete Fourier transform
James H. McClellan, Thomas W. Parks · IEEE Transactions on Audio and Electroacoustics · 1972
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.