Journal ArticleDOI
Eigenvalue and eigenvector decomposition of the discrete Fourier transform
J. McClellan,T. Parks +1 more
Reads0
Chats0
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
More filters
Journal ArticleDOI
Cramer-Rao bounds in the parametric estimation of fading radiotransmission channels
TL;DR: The aim is the derivation of Cramer-Rao lower bounds for the joint estimation of all those channel parameters that impact signal detection, namely, carrier phase, carrier frequency offset, frequency rate of change, signal amplitude, fading power, and Gaussian noise power.
Journal ArticleDOI
Random Discrete Fractional Fourier Transform
Soo-Chang Pei,Wen-Liang Hsue +1 more
TL;DR: This letter proposes a random discrete fractional Fourier transform (RDFRFT) kernel matrix with random DFT eigenvectors and eigenvalues, which is illustrated as a security-enhanced image encryption scheme based on the RDFR FT.
Journal ArticleDOI
Discrete cosine transform in error control coding
Ja-Ling Wu,Jiun Shin +1 more
TL;DR: The authors define a new class of real-number linear block codes using the discrete cosine transform (DCT) and show that a subclass with a BCH-like structure can be defined and, therefore, encoding/decoding algorithms for BCH codes can be applied.
Proceedings ArticleDOI
Discrete fractional Fourier transform
Soo-Chang Pei,Min-Hung Yeh +1 more
TL;DR: In this article, a new version of discrete fractional Fourier transform (DFRFT) was proposed, which provides similar transforms as those of continuous FRFT and also holds the rotation properties.
Journal ArticleDOI
Eigenfunctions of Fourier and Fractional Fourier Transforms With Complex Offsets and Parameters
Soo-Chang Pei,Jian-Jiun Ding +1 more
TL;DR: The derived eigenfunctions of the Fourier transform, the fractional FT (FRFT), and the linear canonical transform (LCT) with complex parameters and complex offsets are derived and are found to be the smoothed Hermite-Gaussian functions with shifting and modulation.
References
More filters
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).