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
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Proceedings ArticleDOI
Chirps on finite cyclic groups
Peter G. Casazza,Matthew Fickus +1 more
TL;DR: The basic properties of chirps over finite cyclic groups are discussed, including a way in which they may be used to construct finite tight frames.
Journal ArticleDOI
Multiple-target recognition using the discrete rotational Fourier transform
TL;DR: A new correlator to locate and display multiple different targets when both the reference and the input images contain many different patterns is proposed, based on the 2-D discrete rotational Fourier transform (DRFT), which extends the one-dimensional (1-D) DRFT.
Journal ArticleDOI
Coherent diffraction imaging based on iterative fractional Fourier transform
TL;DR: This method overcomes the limitations of the same-kind methods which require a prior knowledge of the accurate order of fractional Fourier transform, and converges faster and achieves less error.
Proceedings ArticleDOI
Rational-ordered discrete fractional Fourier transform
Wen-Liang Hsue,Soo-Chang Pei +1 more
TL;DR: In this article, the authors investigated the periodicity and eigendecomposition properties of the rational-ordered discrete fractional Fourier transform (RODFRFT) and derived the eigenvalue multiplicities of the RODFFT of order 4/p, where p is its period.
Periodic eigenfunctions of the Fourier transform operator
TL;DR: In this paper, the generalized function (tempered distribution) f on R was shown to be a p-periodic eigenfunction of the Fourier transform operator F, i.e., f(x+ p) = f (x), Ff = λf for some λ ∈ C.
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).