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
On eigenfunctions of continuous and discrete (anti)symmetric multivariate Fourier transforms
TL;DR: In this article, the authors derived various full sets of eigenfunctions of Fourier transform (continuous and discrete sine and cosine Fourier transforms) associated with Hermite polynomials in one variable.
Journal ArticleDOI
Maximal scarring for eigenfunctions of quantum graphs
Gregory Berkolaiko,B. Winn +1 more
TL;DR: In this article, the existence of scarred eigenstates for star graphs with scattering matrices at the central vertex which are either a Fourier transform matrix, or a matrix that prohibits back-scattering was shown.
DissertationDOI
Fourier bases on the skewed Sierpinski gasket
TL;DR: In this paper, the authors demonstrate the construction of Fourier bases for fractal approximations via a construction analogous to the Fast Fourier Transformation (FFT) for skewed Sierpinski gasket and related fractals.
Journal ArticleDOI
X-ray coherent diffraction interpreted through the fractional Fourier transform
TL;DR: In this article, the fractional Fourier transform was used to deal with diffraction of coherent X-ray beams from the Fresnel to the Fraunhofer regime. But the authors did not consider the effect of coherent diffraction on the Fourier wave propagation.
Posted Content
Fourier Codes
TL;DR: In this paper, a new family of error-correcting codes, called Fourier codes, is introduced, which are derived from the eigenstructure of the Fourier number theoretic 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).