Dans cette thèse, les récepteurs de Wiener optimaux et sous-optimaux à rang réduit pour le CDMA sont étudiés. La thèse est divisée en deux partie. Dans la première partie, les récepteurs sous-optimaux consisant d'un égaliseur de Wiener à rang réduit au rythme chip suivi de desétalement sont étudiés. Un égaliseur à rang réduit est un égaliseur pour lequel quelques coefficients seulement sont optimisés. Le rang du filtre est le nombre de coefficient optimisés. Dans la deuxième partie, la performance asymptotique de quelques récepteurs linéaires est evaluée. Pour étudier la performance asymptotique, on suppose que les codes d'étalement sont aléatoires suivant une certaine distribution. Le rapport Signal à Interference plus Bruit (SINR) à la sortie du récepteur peut ainsi être interprété comme une variable aléatoire. Il est possible de démontrer que ces variables aléatoires tendent vers des valeurs deterministes finies quand le facteur d'étalement et le nombre d'utilisateurs tendent vers l'infini de telle façon que leur rapport reste fini. Ces limites peuvent être utilisées pour comprendre les facteurs qui controlent la performance tels que le canal de propagation, le bruit et le facteur de charge. On présente les résultats précédents relatifs au récepteurs de Wiener optimaux à rang réduit. Ces résultats sont après étendus au récepteurs de Wiener sous-optimaux à rang réduit.On démontre que la convergence du SINR d'un récepteur de Wiener à rang réduit vers celui du récepteur à rang plein est très rapide. Dans le dernier chapitre, on étudie la performance asymptotique de la diversité à la transmission combinée avec un récepteur RAKE où un égaliseur MMSE.

This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schrödinger operators with bounded potentials. We also consider normal Riemannian coverings and show that projecting and lifting of paths are inverse operations which respect the Wiener measure.

Diss.--Wien, 1998. / Bibliogr. p. 221-229. Index.

One of the basic questions in harmonic analysis is to study the decay properties of the Fourier transform of measures or distributions supported on thin sets in Rn. When the support is a smooth enough manifold, an almost complete picture is available. One of the early results in this direction is the following: Let f in Cc∞(dσ), where dσ is the surface measure on the sphere Sn-1 Rn.Then the modulus of the Fourier transform of fdσ is bounded above by (1+|x|)(n-1)/2. Also fdσ in Lp(Rn) for all p > 2n/(n-1) . This result can be extended to compactly supported measure on (n-1)-dimensional manifolds with appropriate assumptions on the curvature. Similar results are known for measures supported in lower dimensional manifolds in Rn under appropriate curvature conditions. However, the picture for fractal measures is far from complete. This thesis is a contribution to the study of asymptotic properties of the Fourier transform of measures supported in sets of fractal dimension 0 < α < n for p ≤ 2n/α. In 2004, Agranovsky and Narayanan proved that if μ is a measure supported in a C1-manifold of dimension d < n, then the Fourier transform of μ is not in Lp(Rn) for 1 ≤ p ≤ 2n/d. We prove that the Fourier transform of a measure μ supported in a set E of fractal dimension α does not belong to Lp(Rn) for p≤ 2n/α. As an application we obtain Wiener-Tauberian type theorems on Rn and M(2). We also study Lp-asymptotics of the Fourier transform of fractal measures μ under appropriate conditions and give quantitative versions of the above statement by obtaining lower and upper bounds for the following limsup L∞ L-k∫|x|≤L|(fdµ)^(x)|pdx

Dans ce travail de thèse, nous nous intéressons à certaines propriétés d'une classe de processus stochastiques à accroissements stationnaires et autosimilaires. Ces processus sont représentés par des intégrales multiples de Wiener-Itô. Dans le premier chapitre, nous étudions les propriétés géométriques des trajectoires de ce type de processus. En particulier, nous obtenons un développement en ondelettes presque-sûr. Celui-ci permet alors de trouver une borne supérieure pour le module de continuité uniforme, une borne supérieure pour le comportement asymptotique du processus et un résultat presque-sûr concernant les coefficients ponctuel et local de Hölder. De plus, nous obtenons des bornes inférieures et supérieures pour les dimensions de Hausdorff du graphe et de l'image des versions multidimensionnelles anisotropes de la classe de processus considérée. Dans le deuxième et le troisième chapitre de cette thèse, nous nous intéressons au calcul différentiel stochastique relatif au processus de Rosenblatt. A l'aide de la théorie des distributions de Hida, nous définissons une intégrale stochastique par rapport au processus de Rosenblatt. Nous obtenons une formule d'Itô pour certaines fonctionnelles du processus de Rosenblatt. Nous calculons explicitement la variance de l'intégrale stochastique par rapport au processus de Rosenblatt pour une classe spécifique d'intégrandes aléatoires. Enfin, nous comparons l'intégrale introduite avec d'autres définitions utilisées dans la littérature et procédons à une étude fine des termes résiduels faisant le lien entre ces différentes définitions. / In this PhD thesis, we are concerned with some properties of a class of self-similar stochastic processes with stationary increments. These processes are represented by multiple Wiener-Itô integrals. In the first chapter, we study geometric properties of the sample path of this type of processes. Specifically, we obtain an almost sure wavelet expansion which, in turn, allows us to compute an upper bound for the uniform modulus of continuity, an upper bound for the asymptotic growth at infinity of the processes and the almost sure values of the pointwise and local Hölder exponents at any points. Moreover, we obtain lower and upper bounds for the Hausdorff dimensions of the graph and the image of multidimensional anisotropic versions of the class of processes previously considered. In the second and in the third chapters, we are interested in the stochastic calculus with respect to the Rosenblatt process. Using Hida distributions theory, we define a stochastic integral with respect to the Rosenblatt process. We obtain an Itô formula for some functional of the Rosenblatt process. We compute explicitly the variance of the stochastic integral with respect to the Rosenblatt process for a specific class of stochastic integrands. At last, we compare the considered integral with other definitions used in the literature and provide a careful analysis of the residual terms linking the different definitions of integrals.

A eletromiografia consiste no estudo do movimentos dos músculos através dos sinais elétricos emitidos pelos mesmos. Esses sinais são captados por meio de eletrodos (de surpefície ou de agulha), sendo muito suscetíveis a variações e interferências não relacionadas diretamente com o movimento muscular (ruídos). Visando obter dados qualitativamente confiáveis, o processamento digital de sinais fornece como ferramentas os filtros ótimos e adaptativos, que são utilizados quando o sinal desajado está contaminado por ruído. Com a finalidade de diminuir o ruído presente no sinal eletromiográfico, foram implementados os filtros de wiener e wiener adaptativo ao algoritmo LMS (least mean square), tendo a análise da relação sinal/ruído dos sinais obtidos demonstrado que não há diferença significativa entre os filtros. Como conclusão, no tratamento de sinais eletromiográficos, pode-se aplicar tanto o filtro de wiener como o de wiener adaptativo, observando-se que este último apresenta a vantagem de consumir menos tempo de processamento. / Electromyography is the study of muscle moviments through the electrical signal that they emanate. These signals are detected with eletrodes (surface or needle), where variations and interferences not directly related with movement are present (noises). Digital signal processing provides optimal and adaptative filters with the aim to get qualitative reliable data. The filters are used when desired signal is corrupted by noise. With the purpose of noise reduction in electromyography signal, wiener and adaptative wiener filters (the last one with least mean square algorithm) were implemented. However, signal-to-noise ratio analysis gave evidence that there is no significative difference between both the filters. As conclusion, in electromygraphy signal treatment, wiener and adaptative wiener filters could be used, with the only difference that the last one takes less processing time.

Este trabalho tem por objetivo a investigação do comportamento de equipamentos de radiodiagnóstico em termos da qualidade da imagem produzida e a subseqüente aplicação desses resultados na otimização do desempenho de esquemas computacionais de auxílio ao diagnóstico, também conhecidos como esquemas CAD (do inglês, Computer-Aided Diagnosis). A principal meta consiste no desenvolvimento de técnicas de pré-processamento para imagens mamográficas digitalizadas que as realçasse de acordo com as características e limitações dos equipamentos utilizados na sua aquisição. A proposta está dividida em duas etapas. Na primeira, foram determinadas as características relativas tanto à resolução espacial como à resolução de contraste de diversos equipamentos mamográficos, avaliadas respectivamente pelas funções de transferência óptica e espectros de Wiener do ruído. Isto permitiu, numa segunda etapa, o desenvolvimento de um filtro digital específico para o pré-processamento de diferentes conjuntos de mamogramas digitais, separados de acordo com os equipamentos utilizados no processo de aquisição. Dessa forma, cada imagem mamográfica teve sua qualidade melhorada de acordo com as características do equipamento que a gerou, determinadas na primeira etapa. Essas imagens, depois de realçadas, foram utilizadas em um esquema CAD previamente desenvolvido, onde pôde ser observada uma melhora em até 12% no seu desempenho quando comparado aos resultados obtidos com imagens mamográficas não realçadas. / The purpose of this work is to evaluate the quality of radiological equipment and their images in order to use these evaluations to improve the performance of a computer-aided diagnosis (CAD) scheme. The mean idea is about the development of image processing techniques to enhance digital mammograms according to the characteristics of the X-ray unit used for image acquisition. This work is basically divided in two parts. In the first one, it were determined the characteristics related to spatial and contrast resolution of several mammographic equipment, evaluated respectively from the optical transfer function and noise Wiener spectrum. This evaluation allowed, in a second part, the development of a preprocessing technique to enhance different set of digital mammographic images, gathered according to the equipment used on its acquisition process. Thus, each mammographic image had its quality improved in conformity with the characteristics of the equipment used on its acquisition, determined in the first part of this work. These images, after the enhancement process, were used on a previously developed CAD scheme. It was observed an improvement of 12% on the CAD performance using pre-processed mammograms compared to the results obtained when using non-enhanced mammographic images.

Nous étudions des problèmes d'interpolation dans des espaces de fonctions analytiques et notamment les espaces de Paley-Wiener.Nous démontrons que l'opérateur de restriction associé à une suite de nombres complexes supposée a priori N-Carleson dans tout demi-plan, définit un isomorphisme entre l'espace de Paley-Wiener et un certain espace de suites (construit à l'aide de différences divisées) si et seulement si la suite en question vérifie certaines conditions, notamment la condition de Muckenhoupt. Ce résultat généralise un résultat de Lyubarskii et Seip de 1997.Nous montrons également que toute suite minimale dans l'espace de Paley-Wiener et telle que l'intersection avec tout demi-plan vérifie la condition de Carleson, est une suite d'interpolation dans tout espace de Paley-Wiener "plus grand", au sens du type exponentiel. Ce dernier résultat s'étend à l'interpolation pondérée et s'applique à la Théorie du contrôle. / We study interpolation problems in spaces of analytic functions and in particular in Paley-Wiener spaces.We show that the restriction operator associated to some N-Carleson sequence is an isomorphism between the Paley-Wiener space and a certain space of sequences (contructed with the help of divided differences) if and only if the sequence satisfies some conditions, in particular the Muckenhoupt condition. This result is a generalization of a theorem of Lyubarskii and Seip obtained in 1997.We also show that every minimal sequence in PW such that the intersection with every half-plane satisfies the Carleson condition is actually an interpolating sequence in every “bigger” space in the sense of the exponential type. This result can be extended to weighted interpolation and has an application in Control Theory.

No description available.

It is shown that multigroup transport equations with nondiagonal cross section matrices arise when the modal approximation is applied to energy dependent transport equations. This work is a study of such equations for the case that the cross section matrix is nondiagonalizable. For the special case of a two-group problem with a noninvertible scattering matrix, the problem is solved completely via the Wiener-Hopf method. For more general problems, generalized Chandrasekhar H equations are derived. A numerical method for their solution is proposed. Also, the exit distribution is written in terms of the H functions. / Ph. D. / incomplete_metadata