Journal ArticleDOI
Eigenvalue and eigenvector decomposition of the discrete Fourier transform
J. McClellan,T. Parks +1 more
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The eigenvalues of a suitably normalized version of the discrete Fourier transform (DFT) are {1, -1,j, -j} and an eigenvector basis is constructed for the DFT.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 {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.read more
Citations
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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
TL;DR: It is proved that for any of the SOPA, the OPA, or the Gram-Schmidt algorithm the output Hermite-Gaussian-like orthonormal eigenvectors are invariant under the change of the input initial orthon formalisms.
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The $\mathfrak {su}(2)_\alpha $ Hahn oscillator and a discrete Fourier–Hahn transform
TL;DR: In this article, the authors define the quadratic algebra which is a one-parameter deformation of the Lie algebra extended by a parity operator, and investigate a model of the finite one-dimensional harmonic oscillator based upon this algebra.
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Real Discrete Fractional Fourier, Hartley, Generalized Fourier and Generalized Hartley Transforms With Many Parameters
Wen-Liang Hsue,Wei-Ching Chang +1 more
TL;DR: This paper proposes reality-preserving fractional versions of the discrete Fourier, Hartley, generalized Fouriers, and generalized Hartley transforms, which have random outputs and many parameters and thus are very flexible.
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Research progress on discretization of fractional Fourier transform
Ran Tao,Feng Zhang,Yue Wang +2 more
TL;DR: A summary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented and it is hoped to offer a doorstep for the readers who are interested in the fractionsal Fouriers transform.
References
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Journal ArticleDOI
The finite Fourier transform
TL;DR: In this paper, the finite Fourier transform of a finite sequence is defined and its elementary properties are developed, and the convolution and term-by-term product operations are defined and their equivalent operations in transform space.
Journal ArticleDOI
A short bibliography on the fast Fourier transform
TL;DR: A guided tour of the fast Fourier transform,” IEEE Spectrum (to be published).