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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Proceedings ArticleDOI
Multiuser communication based on the discrete fractional fourier transform
TL;DR: A multiuser communication technique based on the discrete fractional Fourier transform (DFrFT) is discussed, which uses eigenvectors of the DFrFT transform matrix as user sequences which are transmitted over a real adder channel.
Journal ArticleDOI
A Review of Fault Diagnosis Methods for Rotating Machinery Using Infrared Thermography
TL;DR: In this article , the authors summarized the development and application of IRT as a noncontact and non-invasive tool for equipment condition monitoring and fault diagnosis, and introduced the basic theory of infrared thermography, image processing technology and fault detection methods of rotating machinery in detail.
Spectogram Prediction with Neural Networks
TL;DR: The main contribution of this article is to show that the proposed model for spectrogram magnitude prediction is trainable, and the coefficients can be adapted to particular problems.
Proceedings ArticleDOI
The generalized discrete fractional fourier transforms
TL;DR: The GDFRFT is developed by factorizing the generalized discrete fractional Fourier transform (GDFT) matrix by incorporating the eigenvalues and eigenvectors into the GDFT matrix.
Proceedings ArticleDOI
Adaptive textural segmentation of medical images
TL;DR: In this article, the authors formulated the segmentation process as a configurational optimization problem and discussed the application of simulated annealing optimization methods to the solution of this specific optimization problem.
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).