Search results for "Hadamard transform"
showing 10 items of 10 documents
Some new Hadamard designs with 79 points admitting automorphisms of order 13 and 19
2001
Abstract We have proved that there exists at least 2091 mutually nonisomorphic symmetric (79,39,19)-designs. In particular, 1896 of them admit an action of the nonabelian group of order 57, and an additional 194 an action of the nonabelian group of order 39.
SPECTRAL GEOMETRY OF SPACETIME
2000
Spacetime, understood as a globally hyperbolic manifold, may be characterized by spectral data using a 3+1 splitting into space and time, a description of space by spectral triples and by employing causal relationships, as proposed earlier. Here, it is proposed to use the Hadamard condition of quantum field theory as a smoothness principle.
The Regularized Hadamard Expansion
2017
A local expansion is proposed for two-point distributions involving an ultraviolet regularization in a four-dimensional globally hyperbolic space-time. The regularization is described by an infinite number of functions which can be computed iteratively by solving transport equations along null geodesics. We show that the Cauchy evolution preserves the regularized Hadamard structure. The resulting regularized Hadamard expansion gives detailed and explicit information on the global dynamics of the regularization effects.
Tensor tomography on Cartan–Hadamard manifolds
2017
We study the geodesic X-ray transform on Cartan-Hadamard manifolds, and prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity. This work extends the results of Lehtonen (2016) to dimensions $n \geq 3$ and to the case of tensor fields of any order.
Electric quantum walks in two dimensions
2015
We study electric quantum walks in two dimensions considering Grover, Alternate, Hadamard, and DFT quantum walks. In the Grover walk the behaviour under an electric field is easy to summarize: when the field direction coincides with the x or y axes, it produces a transient trapping of the probability distribution along the direction of the field, while when it is directed along the diagonals, a perfect 2D trapping is frustrated. The analysis of the alternate walk helps to understand the behaviour of the Grover walk as both walks are partially equivalent; in particular, it helps to understand the role played by the existence of conical intersections in the dispersion relations, as we show th…
Electrostatically operated micromirrors for a Hadamard transform spectrometer
2002
The paper presents the development of a linear micromirror array which can be used as a switchable entrance mask for a double-array Hadamard transform spectrometer. In addition to the detector array the double-array spectrometer has a linear multi-slit array realised by independently switchable micromirrors at the entrance side. Two different switch positions of the electrostatically operated mirrors allow the reflection of light into or away from the spectrometer. With this arrangement (mirror array, concave grating and array detector) and the use of the Hadamard transform principle it is possible to increase the signal-to-noise ratio and the resolution of the system compared to convention…
Diagonal space time hadamard codes with erasure decoding algorithm
2005
A major challenge in the area of space time (ST) codes is to find codes suitable for efficient decoding, thus overcoming the problem of many existing ST code designs which require maximum-likelihood (ML) decoding. A solution could be to apply single-input single-output (SISO) channel codes and theory over temporal channel fading to the multi-input single-output (MISO) code construction and classical suboptimum decoding methods. For these purposes, an ST code construction which allows the use of efficient decoding algorithms is described. We propose a concatenated code, where the inner code is the diagonal ST Hadamard (D-STH) code with Paley constructions and the outer code is an algebraic b…
Improved Bounds for Hermite–Hadamard Inequalities in Higher Dimensions
2019
Let $\Omega \subset \mathbb{R}^n$ be a convex domain and let $f:\Omega \rightarrow \mathbb{R}$ be a positive, subharmonic function (i.e. $\Delta f \geq 0$). Then $$ \frac{1}{|\Omega|} \int_{\Omega}{f dx} \leq \frac{c_n}{ |\partial \Omega| } \int_{\partial \Omega}{ f d\sigma},$$ where $c_n \leq 2n^{3/2}$. This inequality was previously only known for convex functions with a much larger constant. We also show that the optimal constant satisfies $c_n \geq n-1$. As a byproduct, we establish a sharp geometric inequality for two convex domains where one contains the other $ \Omega_2 \subset \Omega_1 \subset \mathbb{R}^n$: $$ \frac{|\partial \Omega_1|}{|\Omega_1|} \frac{| \Omega_2|}{|\partial \Ome…
Hadamard NMR imaging with slice selection
1996
Stochastic NMR imaging is one of the less common NMR imaging techniques. Nevertheless, stochastic rf excitation is characterized by some remarkable features: the rf excitation power is at least two orders of magnitude lower in comparison to conventionally pulsed NMR imaging schemes. Thus, the technique is of interest for imaging of large objects. The systematic noise inherent in images obtained with random noise excitation has been eliminated by using pseudorandom noise together with Hadamard transformation for data evaluation. Data acquisition times are comparable to those of ultrafast imaging techniques. For slice selection, z magnetization is destroyed outside the slice region with speci…
Improved Switching Strategy for Selective Harmonic Elimination in DC-AC Signal Generation via Pulse-Width Modulation
2013
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/870904 Open Access We present an advanced design methodology for pulse-width-modulated (PWM) DC-AC signal generation. Using design methods based on the Walsh transform, AC sinusoidal signals can be approximated by suitable PWM signals. For different AC amplitudes, the switching instants of the PWM signals can be efficiently computed by using appropriate systems of explicit linear equations. However, the equation systems provided by conventional implementations of this approach are typically only valid for a restricted interval of AC amplitudes a…