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Hadamard transform
About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.
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TL;DR: In this article, two algorithms for approximate evaluation of certain Hadamard finite-part integrals, which date back to Grunwald (1867), have been analyzed and the stability of the algorithms is considered and two numerical examples are given.
Abstract: Two algorithms for the approximate evaluation of certain Hadamard finite-part integrals, which date back to Grunwald (1867), have been analysed. It is shown that the quadrature sums are closely related to the finite-part integrals of the Bernstein polynomials. The stability of the algorithms is considered and two numerical examples are given
43 citations
TL;DR: In this paper, the fixed point index was used to study the existence of positive solutions for a system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions.
Abstract: In this paper we use the fixed point index to study the existence of positive solutions for a system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions. Here we use appropriate nonnegative matrices to depict the coupling behavior for our nonlinearities.
43 citations
TL;DR: It is shown that Hadamard transform can be used in RF beamsteering/beamcombining to achieve better performance in terms of average achievable spectral efficiency and low hardware cost using 1- or 2-b resolution APSs.
Abstract: This paper proposes a hybrid structure for multi-stream large-scale multi-input multi-output (MIMO) beamforming systems, in single-user scenario, using a Hadamard radio frequency (RF) codebook with low-bit resolution phase shifters. We show that Hadamard transform can be used in RF beamsteering/beamcombining to achieve better performance in terms of average achievable spectral efficiency and low hardware cost using 1- or 2-b resolution APSs. In contrast, the state-of-the-art RF codebook designs available in the literature requires more than 7-b resolution to achieve the same performance as the proposed scheme, for large antenna arrays with up to 256 elements. The performance gains of the proposed RF codebook design is thoroughly investigated using MATLAB simulations for typical mmWave MIMO system, and the simulation results are closely verified by the analytical expressions.
43 citations
TL;DR: In this article, a multidimensional version of the Hermite-Hadamard inequalities for convex functions on general convex bodies was established using a stochastic approach.
43 citations
01 Jan 1997
TL;DR: In this article, the authors proved the existence of continuous families of complex Hadamard matrices of certain prime dimensions, n = 7, 13, 19, 31, 79 and 79.
Abstract: One proves the existence of continuous families of complex Hadamard matrices of certain prime dimensions, n = 7, 13, 19, 31, 79 This result implies the existence in the corresponding matrix algebras $M\sb{n}$(C) of uncountably many non isomorphic orthogonal pairs of maximal abelian $\sp\*$-subalgebras (MASA's) in the sense of SPopa A main point of interest of our result is that it might produce examples of one parameter families of nonisomorphic subfactors of same index n and same graph $A\sb{\infty}$ The numerical and symbolic computations that motivated this class of examples, as well as their formal construction are presented We are also exploring the possibility of extending this construction to all the primes of the form $n = 3\sp{2k} - 2, (k \ge 1)$
For any prime dimension n one proves that the standard complex Hadamard matrix (which corresponds to the matrix of the Fourier transform of vectors in C$\sp{n}$) is an isolated point among the normalized complex Hadamard matrices of the same dimension We also draw connections to the recent finiteness results of UHaagerup regarding circulant complex Hadamard matrices
43 citations