Hadamard transform

About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.

Hadamard matrices of the Williamson type

Abstract: 1. Introduction. An Hadamard matrix is a square matrix of ones and minus ones whose row (and hence column) vectors are orthogonal. The order n of an Hadamard matrix is necessarily 1, 2 or 4t, with t a positive integer. It has been conjectured that this condition (n = 1, 2 or 4i) also insures the existence of an Hadamard matrix of that order. Constructions have been given for particular values of n and even for various infinite classes of values. While other constructions exist, those given in [l]-[8] exhaust the known values of n. In'particular, R. E. A. C. Paley [5] gave construction methods for various infinite classes of Hadamard matrices and indicated for each value of n = it ^ 200 a construction which would supply an

Image information coding apparatus

Abstract: An image information coding apparatus includes a cut-out or extracting unit for cutting out image information into blocks each having a predetermined size, e.g., 4×4 pixels, a preprocessing unit such as an orthogonal transformation unit (e.g., a Hadamard transformation unit) and a scalar quantization unit for performing predetermined preprocessing of the block as a matrix, a separator for separating a plurality of components (e.g., phase information, amplitude information, and zero information) from each element of the preprocessed matrix, information quantizers for coding individual pieces of information constituted by each component, and a synthesizer for synthesizing coding results.

Some New Hermite-Hadamard Integral Inequalities for Convex functions

Abstract: In this paper, we obtain some new integral inequalities of Hermite-Hadamard type involving two newly introduced convex functions, using a simple analytical technique. A few number of results for special means of real numbers are also deduced for applications.

A new ICI matrices estimation scheme using Hadamard sequence for OFDM systems

Abstract: The intercarrier interference (ICI) matrix for the orthogonal frequency division multiplexing (OFDM) systems usually has a fairly large dimension. The traditional least-square solution based on the pseudo-inverse operation, therefore, has its limitation. In addition, the provision of a sufficiently long training sequence to estimate the complete ICI matrix is not feasible, since it will result in severe throughput reduction. In this paper, we derive a lower bound for the mean-square estimation error among the least-square ICI matrix estimators using different training sequences and prove that the minimum mean-square error (MMSE) optimality is attained when the training sequences in different OFDM blocks are orthogonal to each other, regardless of the sequence length. We also prove that the asymptotical mean-square estimation error using the maximal-length shift-register sequences (m-sequences) as in the existing communication standards is 3 dB larger than that using the perfectly orthogonal sequences for ICI matrix estimation. Thus, we propose to employ the training sequences based on the Hadamard matrix to achieve a highly efficient and optimal ICI matrix estimator with minimum mean-square estimation error among all least-square ICI matrix estimators. Meanwhile, our new scheme involves only square computational complexity, while other existing least-square methods require the complexity proportional to the cube of the ICI matrix size. Analytical and experimental comparisons between our new scheme using Hadamard sequences and the existing method using m-sequences (pseudo-random sequences) show the significant advantages of our new ICI matrix estimator. The proposed method is most suitable for OFDM systems with large amount of subcarriers, using high order of subcarrier modulation, and designed for high-end of RF frequency band, where accurate ICI estimation is crucial.