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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TL;DR: In this paper, some Hadamard-type inequalities involving the product of two convex functions are obtained, which generalize the corresponding results of B.G.Pachpatte.
Abstract: Some Hadamard-type inequalities involving the product of two convex functions are obtained. Our results generalize the corresponding results of B.G.Pachpatte.
49 citations
01 Jan 2008
TL;DR: In this article, a monotonic nondecreasing mapping connected with the Hadamard's inequality for Lipschitzian s-convex mapping in the first sense of one variable is established.
Abstract: In this paper a Hadamard’s type inequality of s–convex function in first sense and s–convex function of 2–variables on the co–ordinates are given. A monotonic nondecreasing mapping connected with the Hadamard’s inequality for Lipschitzian s–convex mapping in the first sense of one variable is established.
49 citations
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TL;DR: This paper presents some new skew-Hadamard matrices of order 52 and improves the known lower bound on the number of the skew- hadamardMatrices of this order.
49 citations
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22 Jul 1994TL;DR: The quadtree code as discussed by the authors allows variable block size inherent in quadtrees and the calculational simplicity of Walsh transform descriptions of nearly uniform blocks of data, and construction of the quadtree is calculationally simple for implementation in a digital system.
Abstract: Two-dimensional data structures are represented by quadtree codes with embedded Walsh transform coefficients. The quadtree code permits both variable block size inherent in quadtrees, and the calculational simplicity of Walsh transform descriptions of nearly uniform blocks of data. Construction of the quadtree is calculationally simple for implementation in a digital system which does a bottom-up determination of the quadtree because Walsh transform coefficients and a measure of the distortion can be recursively calculated using only Walsh transform coefficients from the previous level in the quadtree. Uniform step size quantization, which is optimal for variable length coding and generalized gaussian distributions, permits fast encoding and decoding of quadtree code.
49 citations
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TL;DR: Discrete forms of the Fourier, Hadamard, and Karhunen-Loeve transforms are examined for their capacity to reduce the bit rate necessary to transmit speech signals and these bit-rate reductions are shown to be somewhat independent of the transmission bit rate.
Abstract: Discrete forms of the Fourier, Hadamard, and Karhunen-Loeve transforms are examined for their capacity to reduce the bit rate necessary to transmit speech signals. To rate their effectiveness in accomplishing this goal the quantizing error (or noise) resulting for each transformation method at various bit rates is computed and compared with that for conventional companded PCM processing. Based on this comparison, it is found that Karhunen-Loeve provides a reduction in bit rate of 13.5 kbits/s, Fourier 10 kbits/s, and Hadamard 7.5 kbits/s as compared with the bit rate required for companded PCM. These bit-rate reductions are shown to be somewhat independent of the transmission bit rate.
49 citations