Topic
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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17 Jul 2019
TL;DR: In this paper, the authors extend the results of Alp et al. (q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions by considering the critical point-type inequalities.
Abstract: In this paper, we establish some new results on the left-hand side of the q-Hermite–Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al (q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci., 2018, 30, 193-203), by considering the critical point-type inequalities.
58 citations
01 Jan 1967
TL;DR: The notion of correctness* introduced at the beginning of our century by the French mathematician Hadamard plays an important role in the investigation of the problems of mathematical physics as mentioned in this paper, and one often says that a problem is solved if its correctness is established.
Abstract: The notion of correctness* introduced at the beginning of our century by the French mathematician Hadamard plays an important role in the investigation of the problems of mathematical physics. One often says that a problem is solved if its correctness is established.
58 citations
Patent•
20 Jul 1984TL;DR: In this paper, a modified Walsh-Hadamard transform is used to remove noise and preserve image structure in a sampled image, where image signals representative of the light value of elements of the image are grouped into signal arrays corresponding to blocks of image elements.
Abstract: An improved image processing method uses a modified Walsh-Hadamard transform to remove noise and preserve image structure in a sampled image. Image signals representative of the light value of elements of the image are grouped into signal arrays corresponding to blocks of image elements. These signals are mapped into larger signal arrays such that one or more image signals appear two or more times in each larger array. The larger arrays are transformed by Walsh-Hadamard combinations characteristic of the larger array into sets of coefficient signals. Noise is reduced by modifying--i.e., coring or clipping--and inverting selected coefficient signals so as to recover processed signals--less noise--representative of each smaller signal array. The results exhibit acceptable rendition of low contrast detail while at the same time reducing certain processing artifacts characteristic of the unimproved Walsh-Hadamard block transform.
58 citations
Journal Article•
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TL;DR: A developed software in the area of Coding Theory is presented, using it, codes with given properties can be classified and used for investigations of other discrete structures-combinatorial designs, Hadamard matrices, bipartite graphs etc.
Abstract: In this paper we present a developed software in the area of Coding Theory. Using it, codes with given properties can be classified. A part of this software can be used also for investigations (isomorphisms, automorphism groups) of other discrete structures-combinatorial designs, Hadamard matrices, bipartite graphs etc.
58 citations
Posted Content•
TL;DR: Hadamard coded modulation (HCM) is introduced to achieve low error probabilities in LED-based VLC systems needing high-average optical powers and is well suited to environments requiring dimmer lighting.
Abstract: Visible light communication (VLC) systems using the indoor lighting system to also provide downlink communications require high average optical powers in order to satisfy the illumination needs. This can cause high amplitude signals common in higher-order modulation schemes to be clipped by the peak power constraint of the light emitting diode (LED) and lead to high signal distortion. In this paper we introduce Hadamard coded modulation (HCM) to achieve low error probabilities in LED-based VLC systems needing high average optical powers. This technique uses a fast Walsh-Hadamard transform (FWHT) to modulate the data as an alternative modulation technique to orthogonal frequency division multiplexing (OFDM). HCM achieves a better performance for high illumination levels because of its small peak to average power ratio (PAPR). The power efficiency of HCM can be improved by reducing the DC part of the transmitted signals without losing any information. The resulting so-called DC-reduced HCM (DCR-HCM) is well suited to environments requiring dimmer lighting as it transmits signals with lower peak amplitudes compared to HCM, which are thus subject to less nonlinear distortion. Interleaving can be applied to HCM to make the resulting signals more resistant against inter-symbol interference (ISI) in dispersive VLC links.
57 citations