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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: In this article, the authors present a comprehensive, state-of-the-art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances.
Abstract: The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three chapters, each describing one of three distinct faces of this field whose treatment require various mathematical tools ranging from combinatorics, functional analysis to symbolic computation. Although we firmly believe that these beautiful objects are interesting on their own and worth investigating from a purely mathematical perspective we make considerable efforts to highlight some of their applications we aware of.
46 citations
TL;DR: Four smallest cases among these 17 cases are examined and confirmed the conjecture that all the cyclic Hadamard difference sets have parameter v which falls into one of three types of v.
Abstract: The main conjecture of this article is the following: if a cyclic (v=4n-1, k=2n-1, /spl lambda/=n-1) Hadamard difference set exists, the the value of v must be either a prime, or a product of "twin primes," or one less than a power of 2. Six cases, v=399, 495, 627, 651, 783, and 975, which were once listed as the possible exceptions for v >
46 citations
45 citations
TL;DR: Hadamard transform capillary electrophoresis, which is based on a multiple sample injection technique, was combined with laser-induced fluorometry and utilized in the determination of analytes at subpicomolar levels and the sensitivity was substantially improved by increasing the order, i.e., the number of elements, of the Hadamard matrix.
Abstract: Hadamard transform capillary electrophoresis, which is based on a multiple sample injection technique, was combined with laser-induced fluorometry and utilized in the determination of analytes at subpicomolar levels. The sensitivity was substantially improved by increasing the order, i.e., the number of elements, of the Hadamard matrix. In fact, the signal-to-noise ratio was enhanced 18-fold by the use of a matrix of order 2047. A feasibility study was carried out by computer simulation to study the detection of an average of less than a single molecule in a single injection volume. The signal peak was clearly observable even under conditions at which only 0.3 molecule is present in the volume. Thus, this approach is potentially useful for ultratrace analysis, in which conventional single-injection capillary electrophoresis cannot be applied.
45 citations
TL;DR: A conference matrix of order n is a square matrix C with zeros on the diagonal and ± 1 elsewhere, which satisfies the orthogonality condition CCT = (n − 1)I as mentioned in this paper.
Abstract: A conference matrix of order n is a square matrix C with zeros on the diagonal and ±1 elsewhere, which satisfies the orthogonality condition CCT = (n — 1)I. If in addition C is symmetric, C = CT, then its order n is congruent to 2 modulo 4 (see [5]). Symmetric conference matrices (C) are related to several important combinatorial configurations such as regular two-graphs, equiangular lines, Hadamard matrices and balanced incomplete block designs [1; 5; and 7, pp. 293-400]. We shall require several definitions.
45 citations