This work is concerned with the applicability of several approximation methods (finite section method, Galerkin and collocation methods with maximum defect splines for uniform and non uniform meshes) to operators belonging to the closed subalgebra generated by operators of multiplication bz piecewise continuous functions and convolution operators also with piecewise continuous generating function.

In communication system environment speech signal is corrupted due to presence of additive acoustic noise, so with this distortion the effective communication is degraded in terms of the quality and intelligibility of speech. Now present research is going how effectively acoustic noise can be eliminated without affecting the original speech quality, this tends to be our challenging in this current research thesis work. Here this work proposes multi-tiered detection method that is based on time-frequency analysis (i.e. filter banks concept) of the noisy speech signals, by using standard speech enhancement method based on the proven spectral subtraction, for single channel speech data and for a wide range of noise types at various noise levels. There were various variants have been introduced to standard spectral subtraction proposed by S.F.Boll. In this thesis we designed and implemented a novel approach of Spectral Subtraction based on Minimum Statistics [MinSSS]. This means that the power spectrum of the non-stationary noise signal is estimated by finding the minimum values of a smoothed power spectrum of the noisy speech signal and thus circumvents the speech activity detection problem. This approach is also capable of dealing with non-stationary noise signals. In order to analyze the system in time frequency domain, we have implemented two different filter bank approaches such as Weighted OverLap Added (WOLA) and Fast Fourier Transform Modulated (FFTMod). The proposed systems were implemented and evaluated offline using simulation tool Matlab and then validated their performances based on the objective quality measures such as Signal to Noise Ratio Improvement (SNRI) and Perceptual Evaluation Speech Quality (PESQ) measure. The systems were tested with a pure speech combination of male and female sampled at 8 kHz, these signals were corrupted with various kinds of noises at different noise power levels. The MinSSS algorithm implemented using FFTMod filter bank approach outperforms when compared the WOLA filter bank approach.

L'objet de cette thèse est d'étudier la théorie du transport optimal sur un espace de Wiener abstrait. Les résultats qui se trouvent dans quatre principales parties, portent :Sur la convexité de l'entropie relative. On prolongera des résultats connus en dimension finie, sur l'espace de Wiener muni d'une norme uniforme, à savoir que l'entropie relative est (au moins faiblement) 1-convexe le long des géodésiques induites par un transport optimal sur l'espace de Wiener.Sur les mesures à densité logarithmiquement concaves. Le premier des résultats importants consiste à montrer qu'une inégalité de type Harnack est vraie pour le semi-groupe induit par une telle mesure sur l'espace de Wiener. Le second des résultats obtenus nous fournit une inégalité en dimension finie (mais indépendante de la dimension), contrôlant la différence de deux applications de transport optimal.Sur le problème de Monge. On s'intéressera au problème de Monge sur l'espace de Wiener, muni de plusieurs normes : des normes à valeurs finies, ou encore la pseudo-norme de Cameron-Martin.Sur l'équation de Monge-Ampère. Grâce aux inégalités obtenues précédemment, nous serons en mesure de construire des solutions fortes de l'équation de Monge-Ampère (induite par le coût quadratique) sur l'espace de Wiener, sous de faibles hypothèses sur les densités des mesures considérées

The point of departure of this study is that in the 1930s Oskar Morgenstern, well-known as the co-founder of game theory, was preoccupied by his activities in Austrian economic policy, possibly even more so than with his project to revolutionize economic theory. The main questions to be examined in this regard are, first, to what extent Morgenstern's advice did conform to the teachings of the Austrian school and, second, if he really exerted an influence on economic policy-making in Austria during this period. In order to answer this question the paper draws to a large part on unpublished sources from the Oskar Morgenstern Papers and uses them as a basis for determining Morgenstern's role in a few critical episodes of Austrian economic policy-making. (author's abstract) / Series: Department of Economics Working Paper Series

Cette thèse porte sur le problème d'identification des systèmes non linéaires sur la base des modèles blocs. Deux types de modèles sont considérés ici, ceux de type Hammerstein et ceux de type Wiener. La plupart des solutions antérieures ont été élaborées sous des hypothèses assez contraignantes concernant le sous-système non linéaire du modèle. Celui-ci a souvent été supposé lisse (voire polynomial), inversible et sans mémoire. Les travaux présentés dans cette thèse tentent de repousser ces limites. Dans le cas des systèmes de type Hammerstein, nous élaborons un schéma d'identification qui ne fait aucune hypothèse sur l'élément non linéaire, à l'exception du fait qu'il est sans mémoire et l¥-stable ; ce schéma estime parfaitement (du moins dans la cas idéal) les paramètres du sous-système dynamique linéaire et un nuage de points de la caractéristique de l'élément non linéaire. Ce schéma est ensuite adapté au cas où l'on connaît la structure de l'élément non linéaire ; à ce propos, les non-linéarités statiques affines par morceaux et discontinues jouissent d'une attention particulière. Nous terminons la partie consacrée à l'identification des systèmes de Hammerstein, en abordant le problème des systèmes impliquant un élément non linéaire à mémoire. Deux familles d'éléments de cette nature sont considérées : celle comprenant des éléments hystérétiques non saturés et celle des éléments hystérisis-relais. Le problème est appréhendé à l'aide d'un schéma d'identification dont on établit la consistance en présence de perturbations assimilables à un bruit blanc appliqué en sortie du système. <br /> La dernière partie du mémoire est centrée sur l'identification des systèmes de Wiener, dont l'élément non linéaire n'est pas supposé inversible. A cet effet, nous présentons deux schémas d'identification de type fréquentiel et établissons leur consistance dans les mêmes conditions que précédemment concernant les perturbations. L'exigence d'excitation persistante occupe une place centrale dans cette thèse. Pour procurer cette propriété aux différents schémas d'identifications proposés, il a été fait appel à une famille de signaux d'excitation de type impulsionnelle. Dans ce cadre, un lemme technique est élaboré précisant, pour les systèmes linéaires, le lien entre cette famille de signaux et la propriété d'excitation persistante. L'adaptation de ce lemme au cas des systèmes non linéaires est illustrée dans les différents schémas d'identification.

In a large number of applications arising in various fields of study, time series are approximated using linear MMSE estimates. Such approximations include finite order moving average and autoregressive approximations as well as the causal Wiener filter. In this dissertation, we study two topics related to the estimation of wide sense stationary (WSS) time series using linear MMSE estimates. In the first part of this dissertation, we study the asymptotic behaviour of autoregressive (AR) and moving average (MA) approximations. Our objective is to investigate how faithfully such approximations replicate the original sequence, as the model order as well as the number of samples approach infinity. We consider two aspects: convergence of spectral density of MA and AR approximations when the covariances are known and when they are estimated. Under certain mild conditions on the spectral density and the covariance sequence, it is shown that the spectral densities of both approximations converge in L2 as the order of approximation increases. It is also shown that the spectral density of AR approximations converges at the origin under the same conditions. Under additional regularity assumptions, we show that similar results hold for approximations from empirical covariance estimates. In the second part of this dissertation, we address the problem of detecting interdependence relations within a group of time series. Ideally, in order to infer the complete interdependence structure of a complex system, dynamic behaviour of all the processes involved should be considered simultaneously. However, for large systems, use of such a method may be infeasible and computationally intensive, and pairwise estimation techniques may be used to obtain sub-optimal results. Here, we investigate the problem of determining Granger-causality in an interdependent group of jointly WSS time series by using pairwise causal Wiener filters. Analytical results are presented, along with simulations that compare the performance of a method based on finite impulse response Wiener filters to another using directed information, a tool widely used in literature. The problem is studied in the context of cyclostationary processes as well. Finally, a new technique is proposed that allows the determination of causal connections under certain sparsity conditions.

Le spectrofiltre est un filtre de Wiener utilisé pour isoler le bruit de combustion du moteur Diesel. Ce filtre est déterminé pour chaque point de fonctionnement et nécessite un traitement important des données. Il est donc difficile de mener des études perceptives sur le bruit de combustion obtenu selon plusieurs réglages moteur. Afin de pallier à cet inconvénient, cette thèse a pour objectif de définir un filtre commun qui puisse synthétiser un bruit de combustion en tout point de fonctionnement. Pour cela, une étude perceptive a montré que la substitution du spectrofiltre conventionnel par un autre filtre de Wiener permet la synthèse d'un bruit de combustion. L'utilisation d'un spectrofiltre commun est donc possible. L'analyse modale expérimentale permet d'estimer le filtre de Wiener à partir de données caractéristiques de la structure du moteur. Après analyse sur un signal synthétique, la méthode ESPRIT apparait la plus appropriée, mais nécessite quelques optimisations pour être adaptée aux particularités des spectrofiltres. Les filtres de Wiener de plusieurs régimes sont estimés selon différentes conditions d'estimation, définies par le critère ESTER. Une évolution fictive de l'amortissement selon le régime moteur est observée, et rattachée au fenêtrage temporel effectué dans le calcul du spectrofiltre. Une expérience perceptive est ensuite menée pour identifier si le critère ESTER permet d'estimer des filtres assez précis pour synthétiser des bruits de combustion similaires aux bruits de combustion conventionnels. Les résultats amènent à concevoir le spectrofiltre obtenu au ralenti comme un bon filtre commun, tant d'un point de vue physique que perceptif.

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Geomagnetic storms are primarily driven by the rapid transfer of energy from the solar wind to the magnetosphere. The mechanism of energy transfer involves the merging of the interplanetary magnetic field to the geomagnetic field in a process known as magnetic reconnection. This leads to an influx of energetic, charged particles into the magnetosphere so that current systems are enhanced. Specifically, an increase in the equatorial ring current leads to a decrease in the surface field. Geomagnetic storms are thus characterized by a strong decline in the horizontal components of the geomagnetic field, lasting from several hours to days. The intensity of a storm is described by the disturbed storm-time index, which is essentially a measure of the deviation from the typical quiet day variation along the equator. Severe storms can lead to the disruption of high frequency (HF) communications as a consequence of a strongly perturbed ionosphere. By the same token, the global positioning system (GPS) can become highly unreliable during magnetically disturbed conditions, yielding distance errors as large as 50 meters. The impact of geomagnetic activity and other solar-driven processes on technology systems are collectively known as space weather. Magnetic field sensing thus forms an important part of space weather forecasting and is vital to space science research as a means of improving our understanding of solar wind-magnetosphere interactions. This study examines the use of magnetometers built as SQUIDs (Superconducting Quantum Interference Devices) for monitoring the geomagnetic field for space weather forecasting purposes. A basic theory of superconductivity is presented and subsequently the key aspects governing the operation of SQUIDs are discussed. Space weather is also introduced with respect to the various processes on the sun that perturb the magnetosphere and hence the geomagnetic field. The method of analysis was basically to Fourier-transform the data using the Wiener-Khintchine theorem. A systematic approach to Fourier analysis is thus presented, demonstrating the superiority of the Wiener-Khintchine theorem in noise reduction. The suitability of SQUID magnetometers for space science research is demonstrated by a comparative study between SQUID and fluxgate datasets for magnetic storms during 2011. Strong correlation was observed between the frequency content of the SQUID and fluxgate signals. This result supports South Africa’s SQUID project, currently undertaken as a collaborative effort between SANSA Space Science and the Department of Electrical and Electronic Engineering at Stellenbosch University. This thesis thus lays a foundation for future research involving advanced magnetometry using SQUIDs. / AFRIKAANSE OPSOMMING: Geomagnetiese storms word hoofsaaklik gedryf deur die vinnige oordrag van energie van die sonwind na die magnetosfeer. Die meganisme van energie oordrag behels die samesmelting van die interplanetêre magneetveld met die geomagneetveld, in 'n proses wat bekend staan as magnetiese heraansluiting. Dit lei tot 'n instroming van energieke elektries-gelaaide deeltjies, tot in die magnetosfeer, met die gevolg dat magnetosferiese elektriese stroomstelsels versterk word. 'n Toename in die ekwatoriale ringstrome lei spesifiek tot 'n afname in die horisontale komponent van die geomagnetiese veld. Geomagnetiese storms word dus gekenmerk deur 'n sterk afname in die horisontale komponent van die geomagnetiese veld, ‘n afname wat etlike ure tot dae kan duur. Die intensiteit van 'n storm word beskryf deur die storm-tyd versteurings indeks , 'n maatstaf van die afwyking van die tipiese stil dag magnetiese variasie langs die ewenaar. Ernstige storms kan lei tot die ontwrigting van hoë frekwensie (HF) kommunikasie as 'n gevolg van 'n erg versteurde ionosfeer. Soortgelyk kan die Globale Posisionering Stelsel (GPS) hoogs onbetroubaar word tydens magneties versteurde toestande, en posisiefoute so groot as 50 meter veroorsaak. Die impak van geomagnetiese aktiwiteit en ander sonkrag gedrewe prosesse op tegnologie is gesamentlik bekend as ruimteweer. Magneetveldmetinge vorm dus 'n belangrike deel van ruimteweervoorspelling en is noodsaaklik vir ruimtewetenskaplike navorsing as 'n middel om die sonwind-magnetosfeer interaksies beter te verstaan. Hierdie studie ondersoek die gebruik van SQUID (Engels: Superconducting Quantum Interference Device) magnetometers vir die monitering van die geomagnetiese veld vir ruimteweervoorspellingsdoeleindes. ’n Basiese teorie van supergeleiding word aangebied, waarvolgens die sleutelaspekte van SQUIDs bespreek word. Ruimteweer word ook voorgestel in terme van die verskillende prosesse op die son wat die aarde se magnetosfeer en dus die geomagnetiese veld versteur. Die analisemetode wat hier gebruik word, is om die Fourier-transform van data met die Wiener-Khintchine theorema te bereken. A sistematiese metode vir Fourier-analise word aangebied, wat die superiorireit van die Wiener-Khintchine teorema vir ruisvermindering demonstreer. Die geskiktheid van SQUID magnetometers vir ruimtewetenskaplike navorsing word gedemonstreer deur ’n vergelykende studie tussen SQUID- en vloedhek-datastelle vir magnetiese storms gedurende 2011. Sterk korrelasie is waargeneem tussen die frekwensie-inhoud van die SQUID- en vloedhekseine. Hierdie resultate ondersteun Suid-Afrika se SQUID-projek, wat tans as ’n samewerkingspoging tussen SANSA Space Science en die Departement Elektriese en Elektroniese Ingenieurswese aan die Universiteit van Stellenbosch bedryf word. Hierdie tesis lê ’n fondasie vir toekomstige navorsing oor gevorderde magnetometrie met SQUIDs.

Anaerobic digestion, which is the process by which bacteria breakdown organic matter to produce biogas (renewable energy source) and digestate (biofertiliser) in the absence of oxygen, proves to be the ideal concept not only for sustainable energy provision but also for effective organic waste management. However, the production amount of biogas to keep up with the global demand is limited by the underperformance in the system implementing the AD process. This underperformance is due to the difficulty in obtaining and maintaining the optimal operating parameters/states for anaerobic bacteria to thrive with regards to attaining a specific critical population number, which results in maximising the biogas production. This problem continues to exist as a result of insufficient knowledge of the interactions between the operating parameters and bacterial community. In addition, the lack of sufficient knowledge of the composition of bacterial groups that varies with changes in the operating parameters such as temperature, substrate and retention time. Without sufficient knowledge of the overall impact of the physico-environmental operating parameters on anaerobic bacterial growth and composition, significant improvement of biogas production may be difficult to attain. In order to mitigate this problem, this study has presented a nonlinear multi-parameter system modelling of mesophilic AD. It utilised raw data sets generated from laboratory experimentation of the influence of four operating parameters, temperature, pH, mixing speed and pressure on biogas and methane production, signifying that this is a multiple input single output (MISO) system. Due to the nonlinear characteristics of the data, the nonlinear black-box modelling technique is applied. The modelling is performed in MATLAB through System Identification approach. Two nonlinear model structures, autoregressive with exogenous input (NARX) and Hammerstein-Wiener (NLHW) with different nonlinearity estimators and model orders are chosen by trial and error and utilised to estimate the models. The performance of the models is determined by comparing the simulated outputs of the estimated models and the output in the validation data. The approach is used to validate the estimated models by checking how well the simulated output of the models fits the measured output. The best models for biogas and methane production are chosen by comparing the outputs of the best NARX and NLHW models (each for biogas and methane production), and the validation data, as well as utilising the Akaike information criterion to measure the quality of each model relative to each of the other models. The NLHW models mhw2 and mhws2 are chosen for biogas and methane production, respectively. The identified NLHW models mhw2 and mhws2 represent the behaviour of the production of biogas and methane, respectively, from mesophilic AD. Among all the candidate models studied, the nonlinear models provide a superior reproduction of the experimental data over the whole analysed period. Furthermore, the models constructed in this study cannot be used for scale-up purpose because they are not able to satisfy the rules and criteria for applying dimensional analysis to scale-up.

Se buscará analizar cómo a través de la representación de paisajes y descripciones dadas por viajeros que visitaron el Perú en el siglo XIX se definió una imagen del país, mostrando una diversidad de desigualdades en torno a la geografía, habitantes, costumbres y climas respecto a la Costa. Estas descripciones se fueron consolidando en el siglo XIX y se definieron algunas de las construcciones culturales que prevalecen hasta el día de hoy sobre el espacio geográfico. Los Andes se van presentando de una manera desfavorable para la integración nacional a diferencia de la Costa donde es evidente la circulación de bienes y personas entendiéndose como más fluida. Es en la Sierra donde se hace presente la imagen del indio que está acompañado de lo geográfico, donde indios y Andes se encuentran en un mismo vínculo, donde se inventa la tradición del paisaje como un lugar sombrío, deshabitado y nostálgico-, constituyendo un obstáculo que retarda el progreso nacional. Por medio de las descripciones y representaciones de paisajes, ejecutados por viajeros extranjeros como Antonio Raimondi, George Squier y Charles Wiener se intentará analizar los distintos puntos de vista que contribuyeron a la formación del paisaje de la Sierra del Perú en el siglo XIX. / Tesis