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
Citations
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Proceedings ArticleDOI
Bases for the whole sample symmetric filter banks using a complex allpass filter
TL;DR: This work is concerned with the design problem of a whole sample symmetric filter bank where the lowpass and highpass filters are defined in terms of a complex allpass filter.
Journal ArticleDOI
Códigos Corretores de Erros Baseados nas Transformadas Trigonométricas de Corpo Finito
TL;DR: In this paper, a basica consiste em interpretar o calculo de uma transformada como um produto entre um vetor and uma matriz de transformacao especifica.
Ramanujan Theta Function Identities and Quadratic Numbers
TL;DR: In this paper , the discrete Fourier transform can be expressed using Ramanujan theta functions, and new theta function identities, Ramanathan theta identities, and generating functions for the quadratic numbers are derived.
Proceedings ArticleDOI
A new method for channel estimation based on NCP in EUTRA uplink transmission
TL;DR: A new method called NCP-CE (Negative-Cyclic-Prefix-based Channel Estimation), which is more accuracy than traditional method on channel estimation for even-indexed sub-carriers, which boosts performance obviously and brings no increase on complexity.
Proceedings ArticleDOI
Complete analysis of the Eigen functions of Fourier transform
TL;DR: The extended theory of systematic construction of Eigen function concept for sine and cosine functions was applied and the necessary expressions for complex Eigen functions when function f1 is even and function f2 is odd vice versa were derived.
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).