Eigenvalue and eigenvector decomposition of the discrete Fourier transform 论文
1972IEEE Transactions on Audio and Electroacoustics引用 262
Digital Filter Design and ImplementationMathematical Analysis and Transform MethodsNumerical Methods and Algorithms
摘要
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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{1, -1,j, -j}</tex> . 2) An eigenvector basis is constructed for the DFT. 3) The multiplicities of the eigenvalues are summarized for an N×N transform as follows.