Journal ArticleDOI
Eigenvalue and eigenvector decomposition of the discrete Fourier transform
J. McClellan,T. Parks +1 more
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TLDR
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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Journal ArticleDOI
The discrete rotational Fourier transform
TL;DR: A discrete version of the angular Fourier transform is defined and the properties of the transform are presented that show it to be a rotation in time-frequency space, this new transform is a generalization of the DFT.
Journal ArticleDOI
Fractional Fourier-Kravchuk transform
TL;DR: In this article, a model of multimodal waveguides with a finite number of sensor points is introduced, and the fractional finite Fourier-Kravchuk transform is defined to self-reproduce these functions.
Journal ArticleDOI
Convergence of iterative nonexpansive signal reconstruction algorithms
TL;DR: In this paper, a general convergence proof for a general class of iterative signal reconstruction algorithms is presented, which relies on the concept of a nonexpansive mapping in both the time and frequency domains.
Journal ArticleDOI
Discrete fractional Hartley and Fourier transforms
TL;DR: In this paper, the eigenvalues and eigenvectors of the discrete Fourier and Hartley transform matrices are investigated, and the results of the eigendecomposition of the transform matrix are used to define DFRHT and DFRFT.
Journal ArticleDOI
The multiple-parameter discrete fractional Fourier transform
Soo-Chang Pei,Wen-Liang Hsue +1 more
TL;DR: The proposed multiple-parameter discrete fractional Fourier transform (MPDFRFT) is shown to have all of the desired properties for fractional transforms and the double random phase encoding in the MPDFRFT domain significantly enhances data security.
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).