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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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16 Dec 1998TL;DR: In this paper, an efficient decoder for coded orthogonal frequency division multiplex (COFDM) systems is provided by applying j iterations of the fast Hadamard transform, the input vector for the second and subsequent iterations being derived from the result of the immediately preceding iteration.
Abstract: In a coded orthogonal frequency division multiplex (COFDM) system n-bit data words are encoded as 2 m -symbol code words, each symbol having 2 j possible values (e.g. j=3 for octary). An efficient decoder for these code words is provided by applying j iterations of the fast Hadamard transform, the input vector for the second and subsequent iterations being derived from the result of the immediately preceding iteration.
56 citations
TL;DR: In this paper, a system of orthogonal functions known as Walsh functions, which assume only the values +1 and −1, are presented as a tool appropriate for the analysis of well-log data.
Abstract: A system of orthogonal functions, known as Walsh functions, which assume only the values +1 and −1, are presented as a tool appropriate for the analysis of well-log data. Many of the characteristics of these rectangular waveforms, such as discrete transitions in signal level, make them ideal for processing borehole data. Using the generalized Fourier transform, the basic equations for the Walsh transform and Walsh power spectrum are developed showing how the energy in a given signal is distributed among these rectangular wave components. As a first application of the Walsh transform to logging data, a method of computeraided rock boundary identification is developed and demonstrated on a set of well logs from a continental basalt sequence. This technique provides a fast, simple yet accurate means of dividing well-log data into groups of measurements corresponding to different rock units.
56 citations
TL;DR: In this article, the authors proposed a scheme to implement the discrete Hadamard walk in one dimension using a coherent macroscopic sample of ultracold atoms, Bose-Einstein condensate (BEC).
Abstract: We propose a scheme to implement the simplest and best-studied version of the quantum random walk, the discrete Hadamard walk, in one dimension using a coherent macroscopic sample of ultracold atoms, Bose-Einstein condensate (BEC). Implementation of the quantum walk using a BEC gives access to the familiar quantum phenomena on a macroscopic scale. This paper uses a rf pulse to implement the Hadamard operation (rotation) and stimulated Raman transition technique as a unitary shift operator. The scheme suggests the implementation of the Hadamard operation and unitary shift operator while the BEC is trapped in a long Rayleigh range optical dipole trap. The Hadamard rotation and a unitary shift operator on a BEC prepared in one of the internal states followed by a bit-flip operation, implements one step of the Hadamard walk. To realize a sizable number of steps, the process is iterated without resorting to intermediate measurement. With current dipole trap technology, it should be possible to implement enough steps to experimentally highlight the discrete quantum random walk using a BEC leading to further exploration of quantum random walks and its applications.
56 citations
TL;DR: In this paper, Hermite-Hadamard type inequalities involving Hadamard fractional integrals for the functions satisfying monotonicity, convexity and s-e-condition are studied.
Abstract: In this paper, Hermite-Hadamard type inequalities involving Hadamard fractional integrals for the functions satisfying monotonicity, convexity and s-e-condition are studied. Three classes of left-type Hadamard fractional integral identities including the first-order derivative are firstly established. Some interesting Hermite-Hadamard type integral inequalities involving Hadamard fractional integrals are also presented by using the established integral identities. Finally, some applications to special means of real numbers are given. MSC: 26A33; 26A51; 26D15
56 citations
TL;DR: In this paper, the generalized proportional Hadamard fractional integral (GPHF) integral operator with parameter and the proportionality index was used to obtain the Gruss type inequality.
Abstract: In the article, we describe the Gruss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integral operators with nonlocal kernel have diversified applications. Our obtained results show the computed outcomes for an exceptional choice to the GPHF integral operator with parameter and the proportionality index. Additionally, we illustrate two examples that can numerically approximate these operators.
55 citations