Dans cette étude, nous nous penchons sur le modèle Lotka-Volterra, qui est un des premiers modèles prédateur-proie basés sur des principes mathématiques. Le mémoire s'inscrit dans le cadre de la modélisation stochastique du système Lotka-Volterra, c'est-à-dire notre modèle prend en considération que les tailles des populations de proies et de prédateurs sont des variables aléatoires. L'objectif principal est de faire de l'inférence statistique et de la simulation numérique à partir des modèles construits. Nous nous intéressons également à analyser la probabilité d'extinction pour chaque population. Nos modèles sont basés sur certaines propriétés du système déterministe Lotka-Volterra, ainsi que des propriétés des processus de Poisson non homogènes et des processus de naissance et mort non homogènes. Le dernier chapitre de ce mémoire est consacré à l'estimation de paramètres et son étude à partir de simulations numériques. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : système Lotka-Volterra, processus de Poisson non homogène, processus de naissance et mort non homogène, modélisation stochastique, estimation de paramètres, interaction prédateur-proie.

Acoustic echo cancelation (AEC) composes a fundamental property of speech processing to enable a pleasant telecommunication conversation. Without this property of the telephone the communicator would hear an annoying echo of his own voice along with the speech from the other communicator. This would make a conversation through any telecommunication device an unpleasant experience. AEC has been subject of interest since 1950s in the telecom industry and very efficient solutions were devised to cancel linear echo. With the advent of low cost hands free communication devices the issue of non linear echo became prominent because these devices use cheap loudspeakers that produce artifacts in addition to the desired sound which will cause non linear echo that cannot be cancelled by linear echo cancellers. In this thesis a Harmonic Distortion Residual Echo Cancelation algorithm has been chosen for further investigations (HDRES). HDRES has many of those features that are desirable for an algorithm which is dealing with nonlinear acoustic echo cancelation, such as low computational complexity and fast convergence. The algorithm was first implemented in Matlab where it was tested and modified. The final result of the modified algorithm was then implemented in C and integrated with a complete AEC system. Before the implementation a number of measurements were done to distinguish the nonlinearities that were cause by the mobile phone loudspeaker. The measurements were performed on three different mobile pones which were documented to have problems with nonlinear acoustic echo. The result of this thesis has shown that it might be possible to use an adaptive filter, which has both low complexity and fast convergence, in an operating AEC system. However, the request for such a system to work would be that a doubletalk detector is implemented along with the adaptive algorithm. That way the doubletalk situation could be found and the adaptation of the algorithm could be stopped. Thus, the major part of the speech would be saved.

This research was done to develop tools to predict parametric roll motion of ships in regular and irregular sea and provide guidelines to avoid parametric roll during initial design stage. A post Panamax hull form (modified C11 Hull form, Courtesy of MARIN) was used to study parametric roll in ships. The approach of the study has been to simplify the roll equation of motion to a single degree of freedom equation so as to utilize the tools available to analyze the system retaining the non-linear character of the system. The Hill’ equation is used to develop highly accurate stability boundaries in the Ince-Strutt Diagram. The effect of non-linear damping has also been incorporated into the chart for the first time providing a simple method to predict the bounded roll motion amplitude. Floquet theory is also extended to predict parametric roll motion amplitude. Forward speed of the vessel has been treated as a bifurcation parameter and its effects studied both in head and following sea condition. In the second half of the research, parametric roll of the vessel in irregular sea is investigated using the Volterra Quadratic model. GM variation in irregular sea was obtained using transfer functions of the Volterra model. Heave and pitch coupling to roll motion was also studied using this approach. Sensitivity studies of spectral peak period and significant wave height on roll motion amplitude were also carried out. Forward speed effects were also evaluated using the Volterra approach. Based on the study, the Hill’s equation approach was found to give more accurate prediction of parametric roll in regular sea. The boundaries in the stability chart were more accurately defined by the Hill’s equation. The inclusion of non-linear damping in the stability chart gave reasonably accurate bounded motion amplitude prediction. The Volterra approach was found to be a good analytical prediction tool for parametric roll motion in irregular sea. Using the Volterra model, it was found that there is a high probability of parametric roll when the spectral modal period is close to twice the natural period of roll.

Digital satellite communication systems are equipped with nonlinear amplifiers such as travelling wave tube (TWT) amplifiers at or near saturation for better efficiency. The TWT exhibits nonlinear distortion in both amplitude and phase (AM/AM and AM/PM) conversion, respectively. That is, in the digital satellite communication the transmission is disturbed not only by the non-linearity of transmitter amplifier, but also by the inter-symbol interference (ISI) with additive white Gaussian noise. To compensate the non-linearity of the transmitter amplifier and ISI, in this thesis, a new nonlinear compensation scheme consists of the predistorter and adaptive third-order Volterra-based equalizer, with the inverse QRD-RLS (IQRD-RLS) algorithm, which are located before and after the nonlinear channel, is proposed respectively. The third-order Volterra filter (TVF) equalizer based on the IQRD-RLS algorithm achieve superior performance, in terms of convergence rate, steady-state mean-squared error (MSE), and numerically stable. They are highly amenable to parallel implementation using array architectures, such as systolic arrays. The computer simulation results using the M-ary PSK modulation scheme are carried out the signal¡¦s constellation diagrams, the learning curve of the MSE and the bit error rate (BER) are compared with conventional least mean square (LMS), gradient adaptive lattice (GAL) and adaptive LMS with lattice pre-filter algorithms.

This study presents the results of an extraction of the 2nd-order nonlinear responses from model test data. Emphasis is given on the effects of assumptions made for the Gaussian and non-Gaussian input on the estimation of the 2nd-order response, employing the quadratic Volterra model. The effects of sea severity and data length on the estimation of response are also investigated at the same time. The data sets used in this study are surge forces on a fixed barge, a surge motion of a compliant mini TLP (Tension Leg Platform), and surge forces on a fixed and truncated column. Sea states are used from rough sea (Hs=3m) to high sea (Hs=9m) for a barge case, very rough sea (Hs=3.9m) for a mini TLP, and phenomenal sea (Hs=15m) for a truncated column. After the estimation of the response functions, the outputs are reconstructed and the 2nd order nonlinear responses are extracted with all the QTF distributed in the entire bifrequency domain. The reconstituted time series are compared with the experiment in both the time and frequency domains. For the effects of data length on the estimation of the response functions, 3, 15, and 40- hour data were investigated for a barge, but 3-hour data was used for a mini TLP and a fixed and truncated column due to lack of long data. The effects of sea severity on the estimation of the response functions are found in both methods. The non-Gaussian method for estimation is more affected by data length than the Gaussian method.

In an increasingly crowded frequency spectrum with strong interfering signals, the distortion performance, or the linearity, of RF circuits is key to their ability to reject strong intermodulation terms that can corrupt the weak but desired carrier signal. A standard figure-of-merit for small-signal linearity is the Input/Output Third Order Intercept Point (IIP3/OIP3), which represents the input/output power level at which the power of fundamental frequency (PFUND) become equal to that of the third-order intermodulation product (P3rd). Clearly, a higher IIP3 number yields improved linearity, and is highly desirable for many circuits. The thesis will focus on describing the issues that can stem in telecommunication systems from these non-linearities. These non-linearities can be modeled by using a rigorous mathematical expansion based on the Volterra Series. The thesis will "demystify" the Volterra series so that it could be readily understood by the circuit designer, without over burdening him with too much mathematics. Using this series, the distortion performance of an amplifier will be quantified based on IIP3 metrics as described above. Having identified sources of non-linearities, and quantifying the effect of each non-linearity on total IIP3 of an amplifier, the thesis will focus on mitigating these non-linearity sources to increase the overall IIP3 of an amplifier. The techniques discussed to do this are based on both novel device design as well as novel circuit techniques. The amplifiers under discussion will all be SiGe based, due to their exemplary RF performances (comparable to III-V devices) at the fraction of the cost.

Les systèmes bilinéaires jouent un rôle central dans la représentation des systèmes non-linéaires en tant qu'approximant des systèmes non-linéaires analytiques généraux. Une classe particulière de ces systèmes bilinéaires, dits homogènes, permet de représenter la fonctionnelle entrée-sortie comme une série de Volterra à horizon infini mais de degré fini. L'algorithme d'identification héréditaire jusqu'alors limité aux systèmes linéaires est ici étendu à l'identification de ces systèmes en utilisant une structure canonique de base pour l'approximant de degré deux (quadratique). Une forme NARX multidimensionnelle (Nonlinear AutoRegressive eXogenous input) est exploitée ici pour autoriser l'identification du système par la méthode héréditaire. On montre, sur un exemple académique quadratique, la supériorité de cette approche comparée aux algorithmes classiques.

In this thesis we deal with the degree of ill-posedness of linear operator equations in Hilbert spaces, where the operator may be decomposed into a compact linear integral operator with a well-known decay rate of singular values and a multiplication operator. This case occurs for example for nonlinear operator equations, where the local degree of ill-posedness is investigated via the Frechet derivative. If the multiplier function has got zeroes, the determination of the local degree of ill-posedness is not trivial. We are going to investigate this situation, provide analytical tools as well as their limitations. By using several numerical approaches for computing the singular values of the operator we find that the degree of ill-posedness does not change through those multiplication operators. We even provide a conjecture, verified by several numerical studies, how these multiplication operators influence the singular values of the operator equation. Finally we analyze the influence of those multiplication operators on the opportunities of Tikhonov regularization and corresponding convergence rates. In this context we also provide a short summary on the relationship between nonlinear problems and their linearizations. / Diese Arbeit beschaeftigt sich mit dem Grad der Inkorrektheit linearer Operatorgleichungen in Hilbertraeumen, die sich als Komposition eines vollstetigen linearen Integraloperators mit bekannter Abklingrate der Singulaerwerte und eines Multiplikationsoperators darstellen lassen. Dieser Fall tritt beispielsweise bei nichtlinearen Operatorgleichungen auf, wobei der lokale Inkorrektheitsgrad ueber die Frechetableitung bestimmt wird. Falls die Multiplikatorfunktion Nullstellen hat, so ist die Bestimmung des lokalen Grades der Inkorrektheit nicht einfach. Moeglichkeiten und Grenzen der Analysis fuer diese Situation werden betrachtet. Unterschiedliche numerische Ansaetze fuer die Bestimmung der Singulaerwerte liefern, dass der Grad der Inkorrektheit durch die Multiplikationsoperatoren nicht veraendert wird. Es wird sogar ein Zusammenhang angegeben, wie Multiplikationsoperatoren die Singulaerwerte beeinflussen. Schliesslich werden Moeglichkeiten der Tikhonov-Regularisierung unter Einfluss der Multiplikationsoperatoren untersucht. In diesem Zusammenhang wird auch eine kurze Zusammenfassung zur Beziehung von nichtlinearen Problemen und ihren Linearisierungen gegeben.

No description available.

Cette thèse est consacrée à l'exploitation des propriétés de non circularité et de non gaussianité des signaux en traitement d'antennes.Dans une première partie de cette thèse, nous nous intéressons au contexte de la formation de voies (beamforming) pour la réception d'un signal utile inconnu, dont le vecteur directionnel est connu, corrompu par un bruit potentiellement non circulaire et/ou non gaussien. Dans des études récentes, un beamformer MVDR (Minimum Variance Distortionless Response) linéaire au sens large WL (Widely Linear) exploitant la non circularité au second ordre (SO) des interférences a été introduit et analysé. Cependant, ce beamformer demeure sous optimal pour la réception d'un signal utile non circulaire au SO, du moment où il n'exploite pas la non circularité de ce dernier. C'est ainsi, que notre contribution a porté principalement sur l'introduction, l'étude de performances et la mise en \oe uvre d'un beamformer MVDR WL. Ce dernier, basé sur une décomposition orthogonale originale du signal utile introduisant une contrainte supplémentaire, prend en considération la non circularité du signal utile et celle des interférences. L'étude des performances de ce beamformer a montré que ce dernier améliore toujours les performances en présence de signaux non circulaires. Dans le même contexte et pour la réception de signaux non gaussiens, nous avons introduit et étudié un beamformer MVDR non linéaire de Volterra. Ce beamformer dont les contraintes s'adaptent à la non circularité des brouilleurs, a été étudié à l'ordre trois sous sa forme équivalente GSC. Cette structure, dite complète, prend en compte conjointement des propriétés de non circularité et de non gaussianité des brouilleurs. L'analyse des performances en gains en SINR de ce récepteur est donnée pour la réception d'un signal réel corrompu par des brouilleurs non gaussiens et non circulaires d'ordre deux et quatre. Cette analyse a montré que la prise en considération de ces propriétés améliore toujours les performances. Dans une deuxième partie nous nous intéressons au contexte de détection selon deux volets: Le premier volet consiste en la détection d'un signal utile réel connu de paramètres inconnus, noyé dans un bruit total potentiellement non circulaire au SO et de matrice de covariance inconnue. Ainsi, suivant une approche basée sur le test de rapport de vraisemblance généralisé GLRT (Generalized Likelihood Ratio Test), de nouveaux récepteurs pour la détection d'un signal réel connu avec différents ensembles de paramètres inconnus ont été récemment introduits. Néanmoins, les performances de ces récepteurs, n'ont été que partiellement étudiées. Notre contribution a porté sur l'étude des distributions exactes et asymptotiques des statistiques associées au LRT et au GLRT sous H_0 et H_1. Cette étude a permis de donner les expressions théoriques exactes des probabilités de détection et de fausse alarme des récepteurs LRT, et celles asymptotiques pour certains récepteurs GLRT. Nous avons aussi complété cette analyse par des simulations Monte-Carlo en courbes ROC (Receiver Operating Characterisics) pour l'ensemble des détecteurs GLRT. Le deuxième volet, consiste en la détection de non circularité au SO de signaux aléatoires mono et multidimensionnels complexes. Nous avons donné la distribution asymptotique du GLR de non circularité sous H_0 et H_1 dérivé sous l'hypothèse de distribution gaussienne mais utilisée sous une distribution arbitraire non nécessairement gaussienne des données. Ces données considérées sont indépendantes, mais non nécessairement identiquement distribuées, ce qui permet de traiter des situations pratiques où les données non circulaires sont perturbées par un résidu de fréquence et un bruit additif gaussien circulaire. Cette analyse a été aussi complétée par des courbes ROC.