Showing papers on "Circulant matrix published in 1984"
TL;DR: Suboptimal fast transforms are useful substitutes to the optimal Karhunen-Loeve transform (KLT), and the selection of an efficient approximation for the KLT must be done with respect to some performance criterion that might differ from one application to another as mentioned in this paper.
63 citations
TL;DR: In this article, it was shown that λ(n), σ(n) are between (2n) −1 ( n 4 ) −n 2 and c√n (2.274)−n, where c is a constant, c ( 2.274 ) n ⩽χ(n)/φ(n/φ 2(n 4 ) n 2, and c (5.172) n/μ(n)-⩽4n 2 (n 4 ).
29 citations
TL;DR: This paper presents a fast method for estimating dominant harmonics in a sequence of data and shows that this method is related to “lattice methods” for linear prediction and to Prony’s method for exponential approximation.
Abstract: This paper presents a fast method for estimating dominant harmonics in a sequence of data. In a stochastic sense, the proposed method finds the autoregressive scheme with a pure point spectrum that best describes the data, while from a deterministic point of view, the method is a special case of the Lanczos algorithm for finding eigenvalues of a symmetric matrix. Eigenvalue approximations come into play because every circulant matrix is diagonalized by the discrete Fourier transform matrix, and so using the Lanczos algorithm with the given data as the initial vector on a simple circulant matrix, the eigenvalues that are first approximated are the eigenvalues corresponding to eigenvectors which are dominant in the initial vector. It is shown that this method is related to “lattice methods” for linear prediction and to Prony’s method for exponential approximation.
24 citations
TL;DR: A ternary self-dual code is obtained which is the largest known code meeting the bound of Mallows and Sloane.
Abstract: We discuss [2(p + 1), p + 1] double circulant codes which are the ternary images of the [p + 1,(p + 1)/2] extended quadratic residue codes over GF (9) . Here p is a prime of the form p = 12k \pm 5 . As a special result we obtain a [64, 32,18] ternary self-dual code which is the largest known code meeting the bound of Mallows and Sloane.
22 citations
TL;DR: In this article, the authors derived a simple formula for the number of spanning trees of the circulant graphs and some special cases of the Circulant Graphs are also taken into account.
Abstract: In this paper, we derive a simple formula for the number of spanning trees of the circulant graphs. Some special cases of the circulant graphs are also taken into account.
22 citations
TL;DR: In this article, the authors investigated the matrix equation A m = dl + λJ, where A is a rational circulant and d and λ are rational numbers, I is the identity matrix, and J is the matrix with every entry equal to 1.
13 citations
TL;DR: A particular binary circulant matrix is considered and an explicit form of its inverse is given.
9 citations
TL;DR: For any positive integer n, a necessary and sufficient condition for an n × n r-circulant over the Boolean algebra B = {0, 1} to be idempotent was given in this paper.
6 citations
TL;DR: In this paper, a matrix theoretical method for obtaining molecular symmetry coordinates is described based on the diagonalization of the circulant submatrices of G kinetic and F potential energy matrices representing interaction of equivalent internal coordinates.
5 citations
TL;DR: In this paper, necessary and sufficient conditions for the existence of self dual 2k circulant codes were given, and the number of such codes when these conditions are satisfied was specified.
Abstract: In this paper we give necessary and sufficient conditions for the existence of self dual 2k circulant codes. We specify the number of such codes when these conditions are satisfied.
4 citations
TL;DR: A suitable modification allows the eigenvalues of many different circulant matrices to be found simultaneously, and can be used for the initial portion of a coherent optical matrix inversion system, which can find the inverses of circulants.
Abstract: A coherent optical system for performing continuous Fourier transforms can be modified to perform discrete Fourier transforms. Such a system is capable of diagonalizing circulant matrices presented at its input. The diagonal elements of the new matrix are the eigenvalues of the original matrix. A suitable modification allows the eigenvalues of many different circulant matrices to be found simultaneously. Such a technique can be used for the initial portion of a coherent optical matrix inversion system, which can find the inverses of circulant matrices. The method can also be applied to the problem of inverting Toeplitz matrices in a hybrid digital and optical system.
01 Mar 1984
TL;DR: The optimum Wiener solution, the minimum mean-squared-error (MSE), the convergence condition, and the excess MSE in the steady state are obtained using discrete Fourier transform on the frequency-domain FLMS ADF.
Abstract: In this paper we analyze the convergence behavior of the frequency-domain LMS(FLMS) adaptive digital filter(ADF) using discrete Fourier transform. We obtain the optimum Wiener solution, the minimum mean-squared-error(MSE), the convergence condition, and the excess MSE in the steady state. Also, we study the convergence behavior of the FLMS ADFbased on the concept of a self-orthogonalizing algorithm. By approximating the input autocorrelation matrix as a circulant matrix, we compare the results ofthe LMS and FLMS ADF's.
TL;DR: In this article, the authors considered convolution operators of the form which are integral operators on the whole class, i.e., the kernel is such that for almost all of the convolutions, the characteristic function is the Fourier transform.
Abstract: This article considers convolution operators of the form which are integral operators on the whole class , i.e., the kernel is such that for almost all . An answer is obtained to the following question of Korotkov: if is a convolution operator which is an integral operator on the whole of , does it follow that \lambda\} for any 0$ SRC=http://ej.iop.org/images/0025-5734/48/1/A13/tex_sm_2671_img8.gif/>? Here is the Fourier transform of . An example answering the question in the negative is given by the operator with kernel such that where is the characteristic function of .Bibliography: 4 titles.