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Hermite-Gaussian-like eigenvectors of the discrete Fourier transform matrix based on the singular-value decomposition of its orthogonal projection matrices

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3 Author(s)
Hanna, M.T. ; Dept. of Eng. Math. & Phys., Cairo Univ./Fayoum Branch, Fayoum, Egypt ; Attalla Seif, N.P. ; Ahmed, W.A.E.M.

A technique is proposed for generating initial orthonormal eigenvectors of the discrete Fourier transform matrix F by the singular-value decomposition of its orthogonal projection matrices on its eigenspaces and efficiently computable expressions for those matrices are derived. In order to generate Hermite-Gaussian-like orthonormal eigenvectors of F given the initial ones, a new method called the sequential orthogonal procrustes algorithm (SOPA) is presented based on the sequential generation of the columns of a unitary matrix rather than the batch evaluation of that matrix as in the OPA. It is proved that for any of the SOPA, the OPA, or the Gram-Schmidt algorithm (GSA) the output Hermite-Gaussian-like orthonormal eigenvectors are invariant under the change of the input initial orthonormal eigenvectors.

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Circuits and Systems I: Regular Papers, IEEE Transactions on  (Volume:51 ,  Issue: 11 )