International Telemetering Conference Proceedings / November 04-07, 1991 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Shortened cyclic codes are not cyclic, but many cyclic shifts of various code words are still part of the shortened code set. This paper addresses the probability of false synchronization obtained through polynomial division of a serial shortened cyclic code stream in a “sliding” window correlator.

R.M. Fano. / "November 18, 1948." / Bibliography: p. 13. / Army Signal Corps Contract No. W36-039 sc-32037 Project No. 102B. Dept. of the Army Project No. 3-99-10-022.

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Low frequency radio astronomy has entered a second golden age driven by the development of a new class of large-N interferometric arrays. The low frequency array (LOFAR) and a number of redshifted HI Epoch of Reionization (EoR) arrays are currently undergoing commission and regularly observing. Future arrays of unprecedented sensitivity and resolutions at low frequencies, such as the square kilometer array (SKA) and the hydrogen epoch of reionization array (HERA), are in development. The combination of advancements in specialized field programmable gate array (FPGA) hardware for signal processing, computing and graphics processing unit (GPU) resources, and new imaging and calibration algorithms has opened up the oft underused radio band below 300 MHz. These interferometric arrays require efficient implementation of digital signal processing (DSP) hardware to compute the baseline correlations. FPGA technology provides an optimal platform to develop new correlators. The significant growth in data rates from these systems requires automated software to reduce the correlations in real time before storing the data products to disk. Low frequency, widefield observations introduce a number of unique calibration and imaging challenges. The efficient implementation of FX correlators using FPGA hardware is presented. Two correlators have been developed, one for the 32 element BEST-2 array at Medicina Observatory and the other for the 96 element LOFAR station at Chilbolton Observatory. In addition, calibration and imaging software has been developed for each system which makes use of the radio interferometry measurement equation (RIME) to derive calibrations. A process for generating sky maps from widefield LOFAR station observations is presented. Shapelets, a method of modelling extended structures such as resolved sources and beam patterns has been adapted for radio astronomy use to further improve system calibration. Scaling of computing technology allows for the development of larger correlator systems, which in turn allows for improvements in sensitivity and resolution. This requires new calibration techniques which account for a broad range of systematic effects. And, a deep integration between DSP hardware and software data reduction into a single backend.

This thesis is focused on the application of cross-correlation technique for leak detection and location in medium density polyethylene (MDPE) pipes. A leaking water pipe generates noise that depends primarily on water pressure, pipe characteristics and the leak size and shape. This noise, commonly called leak signals, can be used for the purpose of leak detection and leak location in MDPE pipes. A correlation technique is typically employed to detect, position and characterise these water leaks and is proved to be very efficient for metallic pipes. However, the same is not true for MDPE pipes where the attenuation rate with distance of the leak/source signal is very high, and the generated leak signals are of low frequency and narrow bandwidth. In order to locate leak with good accuracy in MDPE pipes, the correlation process relies on the estimation of speed of leak signals in water/pipe and the time delay between leak signals measured at two locations. For time delay estimation, a correlation function is used. Its accuracy depends upon the sharpness of the correlation peak, type and positioning of sensor, and the processing of signals obtained, which in turn further depends upon the characteristics of leak signals. In MDPE pipes, leak signals are of low frequency and narrow bandwidth; however, their frequency response is not well characterised. Therefore, this thesis presents an analytical model to explain the acoustic characteristics of leak signals in MDPE pipes. The model is used to study the effects of the cut-off frequencies of low, high and band pass digital filters and the selection of acoustic/vibration sensors for the correlation technique. It detailed the importance of the cut-off frequency of the high pass filter and the insensitivity of the correlation function to the cut off frequency of the low pass filter.

M. Tech. Electrical Engineering. / Attempts to find computational efficient ways to identify and extract gunshot impulses from signals. Areas of study include Generalised Cross Correlation (GCC), sidelobe minimisation utilising Least Square (LS) techniques as well as training algorithms using a Reproducing Kernel Hilbert Space (RKHS) approach. It also incorporates Support Vector Machines (SVM) to train a network to recognise gunshot impulses. By combining these individual research areas more optimal solutions are obtainable.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 139-144).

Yangian symmetric correlators can be constructed by the action of Yang-Baxter R operators on trivial basic correlators. The example of a four-point correlator is given in two representations and the construction of the completely connected N point correlator is described. The helicity representation is dicussed and the relation of the four-point correlator to tree-level scattering amplitudes is shown.

L'objectif principal de cette thèse est de généraliser les multizetas au cas où le corps de base Q est remplacé par un corps de nombres quelconque. La motivation derrière cette construction vient des travaux de A. Goncharov sur les corrélateurs de Hodge et de la philosophie plectique de J. Nekovar et A. Scholl. On commence par la construction des fonctions de Green plectiques supérieures. Hecke a prouvé que l'intégration d'une série d'Eisenstein appropriée sur le groupe de classes des idèles du corps de nombres donné, multipliée par un caractère du groupe des classes des idèles, est équale à la fonction L associée à ce caractère. Remplacant la série d'Eisenstein par les fonctions de Green plectiques supérieures, une intégration similaire donne des nouveaux résultats, qui généralisent les multizetas classiques et les multi-polylogarithmes. D'après le principe plectique, un sous-groupe de l'anneau des entiers du corps de nombres donné joue un rôle essentiel dans ces travaux. / The principal objective of this thesis is to generalize multiple zeta values to the case when the ground field Q is replaced by an arbitrary number field. The motivation behind the construction comes from the work of A. Goncharov on Hodge correlators and the plectic philosophy of J. Nekovar and A. Scholl. We start by constructing the higher plectic Green functions. Hecke once proved that the integral of the restriction of a suitable Eisenstein series over $\mathbb{Q}$ to the idele class group of a given number field multipled an idele class character of finite order is equal to the L-function of this charator. By replacing Eisenstein seris with our higher plectic Green functions, a similar integration gives new results, which give the generalization of classical multiple zeta values and multiple polyloarithms. According to the plectic principle, a non-trivial subgroup of the ring of integers of a given number field plays an essential role in this work.

Mirror symmetry is a phenomenon from physics that has inspired a lot of interesting mathematics. In the Landau-Ginzburg setting, we have two constructions, the A and B models, which are created based on a choice of an affine singularity with a group of symmetries. Both models are vector spaces equipped with multiplication and a pairing (making them Frobenius algebras), and they are also Frobenius manifolds. We give a result relating stabilization of singularities in classical singularity to its counterpart in the Landau-Ginzburg setting. The A model comes from so-called FJRW theory and can be de fined up to a full cohomological field theory. The structure of this model is determined by a generating function which requires the calculation of certain numbers, which we call correlators. In some cases the their values can be computed using known techniques. Often, there is no known method for finding their values. We give new computational methods for computing concave correlators, including a formula for concave genus-zero, four-point correlators and show how to extend these results to find other correlator values. In many cases these new methods give enough information to compute the A model structure up to the level of Frobenius manifold. We give the FJRW Frobenius manifold structure for various choices of singularities and groups.