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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: This note investigates the connection between tiling of Abelian groups and constructions of complex Hadamard matrices via a natural tiling construction and finds some necessary conditions to be equivalent to a Dita-type matrix.
Abstract: Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling Abelian groups and constructions of complex Hadamard matrices. First, we recover a recent very general construction of complex Hadamard matrices due to Dita via a natural tiling construction. Then we find some necessary conditions for any given complex Hadamard matrix to be equivalent to a Dita-type matrix. Finally, using another tiling construction, due to Szabo, we arrive at new parametric families of complex Hadamard matrices of order 8, 12 and 16, and we use our necessary conditions to prove that these families do not arise with Dita's construction. These new families complement the recent catalogue of complex Hadamard matrices of small order.
25 citations
25 citations
TL;DR: Through the conformable fractional integral inequalities, this work found some new inequalities of Hermite–Hadamard type for convex functions in the form of classical integrals.
Abstract: In this work, we established new inequalities of Hermite–Hadamard type for convex functions via conformable fractional integrals. Through the conformable fractional integral inequalities, we found some new inequalities of Hermite–Hadamard type for convex functions in the form of classical integrals.
25 citations
25 citations
TL;DR: A novel method based on Hadamard precoding is proposed to reduce the peak-to-average power ratio in optical direct detection OFDM system and is successfully applied to an experimental system of optical direct-detection OFDM signal transmission through fiber.
Abstract: The high peak-to-average power ration (PAPR) values of optical orthogond frequency division multiplexing (OFDM) signal limit the system nonlinear tolerance (NLT). In this paper, a novel method based on Hadamard precoding is proposed to reduce the peak-to-average power ratio in optical direct detection OFDM system. The proposed scheme is successfully applied to an experimental system of optical direct-detection OFDM signal transmission through fiber. In this experiment, the 2.5 Gbit/s binary phase shift keying (BPSK) optical OFDM signals with Hadamard precoding are generated and transmitted though a single mode fiber. The experimental results show that the proposed scheme can reduce PAPR by almost 1.5 dB. Meantime the received sensitivity is improved by 2 dB with 100 km fiber transmission compared with that of an ordinary optical direct detection OFDM system.
25 citations