This thesis is concerned with the development of a slope-feedback coder, the purpose of which is to reduce the bandwidth required for the transmission of telephone-quality speech. Three similar coders, which operate separately on each of the three principal formants in speech, are required. The coding results in a reduction in the speech bandwidth from 3200 cps to 500 cps; the corresponding channel-capacity required is reduced from 32,000 bits per second to 6,200 bits per second. Theoretical statements of the performance of the coder are given showing how it transforms some stylised input signals (e.g. ramp and sinewave). From these statements, it is shown that: a) a single channel for each coder leads to very inferior performance - it is shown that two channels are required, and this gives good performance using much the same bandwidth; b) the signal-to-noise ratio required is moderate. A slope-feedback coder has been constructed, and a technical description of this apparatus is given. Experimental tests of the coder operating on simulated formants justify the theoretical predictions to within a root-mean-square error of twelve percent. This error decreases to six percent if those errors which are most subject to apparatus error are not considered. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The first part of this thesis describes the design and construction of a pulse communications system called delta modulation. A simple transistorized coder and decoder was built to convert speech signals into binary pulses, and back again. This system was tested in several ways: the circuit performance was checked electronically, and the quality of transmission through the system was judged by listening tests and by comparison with special tapes containing controlled amounts of signal and thermal noise. The second part concerns the design and construction of a compressor and expandor that can be used with a delta system in order to improve its transmission quality. A fast-acting compressor and expander was constructed using diode-bridges as non-linear elements. Tests of the two components used "back-to-back" showed a satisfactory matching of their characteristics. If these components were used with the delta modulation system, there would be a considerable increase in the range of signal levels that could be transmitted with reasonable quality. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Thesis (Ph. D.)--Brigham Young University. Dept. of Electrical and Computer Engineering, 2007. / Includes bibliographical references (p. 137-143).

Thesis (M. Eng.)--Carleton University, 1992. / Also available in electronic format on the Internet.

Thesis. 1979. Ph.D.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Vita. / Includes bibliographical references. / Ph.D.

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Ce travail cherche a comprendre comment l'ajout d'une géométrie non euclidienne dans un problème de Schrödinger non linéaire influe sur l'existence et l'unicité des solutions explosives de masse critique. On s'inspire pour beaucoup des travaux de Merle et Raphaël sur la méthode de modulation des paramètres d'invariance géométrique pour une EDP qui possède de bonnes lois de conservations. On s'appuie ici plus particulièrement sur un article de Raphaël et Szeftel qui prouve l'existence et l'unicité d'une solution de masse critique en dimension 2 pour l'équation de Schrödinger non linéaire avec potentiel d'inhomogénéité devant la non-linéarité, et qui explose par ailleurs au maximum de l'inhomogénéité. Dans un premier temps, il s'agit de reprendre la méthode dans son ensemble afin de l'adapter à des cas où le Laplacien n'est plus plat, et est remplacé par un opérateur de type Laplace-Beltrami ou Laplacien généralisé. Ayant mis en avant le rôle de la courbure au point d'explosion, en termes de conditions sur les dérivées de termes métriques, on reprend dans un deuxième temps l'étude dans le cas plus général d'une variété riemannienne. Grâce à un ansatz sur la solution qui intègre maintenant la transformation induite par la métrique, on est capable d'énoncer un résultat d'existence et d'unicité en termes de conditions géométriques sur la variété elle même. Par soucis de simplicité, on se limite néanmoins au rôle local de la métrique, en la supposant globalement définie dans une certaine carte, et asymptotiquement équivalente a la métrique euclidienne. / The present work aims at investigating the effects of a non-euclidean geometry on existence and uniqueness results for critical blow up NLS solutions. We will use many ideas from the works of Merle and Raphaël, particularly ideas from modulation theory which describes a solution in terms of geometric invariants parameters. We will rely more specically on a paper from Raphaël and Szeftel for existence and uniqueness of a critical mass blow up solution in dimension two tothe nonlinear Schrödinger equation with inhomogeneous potential acting on the nonlinearity, and which blows up where the inhomogeneity reaches its maximum. At first, we consider a generalized Laplacian operator and deploy the classical ansatz method to point out difficulties inherited from the non-flat metric terms, and in particular the key role played by the curvature at the blow-up point. In a second part, we reproduce the method when modifying the geometrical ansatz on which the parametrix is constructed, and investigate more precisely what is needed for existence and then uniqueness when dealing with a Laplace-Beltrami operator associated to a riemannian manifold. For simplicity, we shall only consider the role of g locally around the blow up point we are constructing, by assuming g is globally defined in some map, and asymptotically equals the usual euclidean metric.

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