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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Satellite Image Compression using Fractional Fourier Transform
TL;DR: It is observed that discrete fractional Fourier transform is very efficient for obtaining better PSNR around 41 dB at 50% CR while maintaining the higher visual quality of decompressed satellite images.
Journal ArticleDOI
A Low-Complexity Approach to Computation of the Discrete Fractional Fourier Transform
TL;DR: This paper proposes an effective approach to the computation of the discrete fractional Fourier transform for an input vector of any length N that allows to reduce the number of arithmetic operations when calculating the discrete fractionsal Fouriers transform.
Journal ArticleDOI
An uncertainty principle for finite frames
Mark Lammers,Anna Maeser +1 more
TL;DR: In this article, the authors consider the notion of uncertainty for finite frames and obtain a time-frequency measure based on the difference operator inspired by the Gauss-Hermite differential equation, and then find the minimizer of the measure over all equal norm Parseval frames, dependent on the dimension of the space and the number of elements in the frame.
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Comments on "Eigenvector and eigenvalue decomposition of the discrete Fourier transform"
Dissertation
Phase estimation with application to speech analysis-synthesis
TL;DR: Originally published as thesis (Dept. of Electrical Engineering and Computer Science, Sc.D., 1979).
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).