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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: The existence of solutions for a mixed initial value problem of Hadamard and Riemann–Liouville fractional integro-differential inclusions by means of endpoint theory is studied.
42 citations
TL;DR: In this article, the authors used a digital micro-mirror array (DMA) as a computer-controlled 2D Hadamard encoding mask, which is 16 um square and rotatable by ± 10°.
41 citations
TL;DR: Two-dimensional Walsh spectral analysis is presented as a new method of numerically processing the Young's fringes diffraction pattern from a double-exposure speckle photograph, giving results of almost identical accuracy but with substantially reduced computational effort.
Abstract: Two-dimensional Walsh spectral analysis is presented as a new method of numerically processing the Young's fringes diffraction pattern from a double-exposure speckle photograph. The Walsh spectrum of the fringes is more complex than the Fourier spectrum but can be interpreted reliably by further cross correlation of the fringes with square waves. Compared with Fourier spectral analysis, the new technique gives results of almost identical accuracy but with substantially reduced computational effort. The ideas presented have relevance to the general problem of detecting and accurately determining the frequency components of a 2-D sinusoid in the presence of noise.
41 citations
TL;DR: This paper presents a straightforward procedure using Walsh functions to determine the pattern in a binary sequence and when extended to infinite sequences it yields results agreeing with those by the classical probability theory.
Abstract: The concept of a finite binary random sequence does not seem to be covered in the classical foundations of the theory of probability. Solomonoff, Kolmogorov and Chaitin have tried to include this case by considering the lengths of programs required to generate these sequences: a longer program implying more randomness. However this definition is difficult to apply. This paper presents a straightforward procedure using Walsh functions to determine the pattern in a binary sequence. A quantitative measure of randomness has also been proposed. This has been defined as the number of independent data (via the Walsh transform) required to generate the sequence divided by the length of the sequence. However at present this classification procedure is restricted to sequences of length 2k only. When extended to infinite sequences it yields results agreeing with those by the classical probability theory.
41 citations
TL;DR: In this paper, the authors provide an overview of symmetric Hadamard matrices of order 36, showing that the Steiner triple systems of order 15 can be switched into strongly regular graphs.
Abstract: Publisher Summary This chapter provides an overview of symmetric Hadamard matrix of order 36. A square matrix H is a Hadamard matrix if its elements are + 1 and if it is orthogonal. If in addition, H is symmetric, has a constant diagonal I, and has order 36, then H2 = 36I, H = HT, H = A + I, (A−5I) (A+7I) = 0.The chapter explains a method to obtain symmetric Hadamard matrices of order 36 from the 12 Latin squares of order 6, and from the 80 Steiner triple systems of order 15 . The graphs obtained in this way are shown to be nonequivalent with respect to switching, with one exceptional pair. The method consists of counting void and complete sub-graphs, and is capable of wider application. The chapter also explains how graphs of the Steiner type can be switched into strongly regular graphs. Among these graphs, there are 23 that can be made regular with valency 21, whereas all 80 can be made regular with valency I5. This follows from a computer search by which each of the 80 Steiner triple systems appears to contain a 3-factor, that is, a subsystem of 15 triples in which every symbol occurs exactly three times.
41 citations