Linear digital signal processing based around linear, time-invariant systems theory finds substantial application in speech processing. The linear acoustic source-filter theory of speech production provides ready biomechanical justification for using linear techniques. Nonetheless, biomechanical studies surveyed in this thesis display significant nonlinearity and non-Gaussinity, casting doubt on the linear model of speech production. In order therefore to test the appropriateness of linear systems assumptions for speech production, surrogate data techniques can be used. This study uncovers systematic flaws in the design and use of exiting surrogate data techniques, and, by making novel improvements, develops a more reliable technique. Collating the largest set of speech signals to-date compatible with this new technique, this study next demonstrates that the linear assumptions are not appropriate for all speech signals. Detailed analysis shows that while vowel production from healthy subjects cannot be explained within the linear assumptions, consonants can. Linear assumptions also fail for most vowel production by pathological subjects with voice disorders. Combining this new empirical evidence with information from biomechanical studies concludes that the most parsimonious model for speech production, explaining all these findings in one unified set of mathematical assumptions, is a stochastic nonlinear, non-Gaussian model, which subsumes both Gaussian linear and deterministic nonlinear models. As a case study, to demonstrate the engineering value of nonlinear signal processing techniques based upon the proposed biomechanically-informed, unified model, the study investigates the biomedical engineering application of disordered voice measurement. A new state space recurrence measure is devised and combined with an existing measure of the fractal scaling properties of stochastic signals. Using a simple pattern classifier these two measures outperform all combinations of linear methods for the detection of voice disorders on a large database of pathological and healthy vowels, making explicit the effectiveness of such biomechanically-informed, nonlinear signal processing techniques.

This thesis examines second-order optical nonlinear wave mixing processes in domain-disordered quasi-phase matching waveguides and evaluates their potential use in compact, monolithically integrated wavelength conversion devices. The devices are based on a GaAs/AlGaAs superlattice-core waveguide structure with an improved design over previous generations. Quantum-well intermixing by ion-implantation is used to create the quasi-phase matching gratings in which the nonlinear susceptibility is periodically suppressed. Photoluminescence experiments showed a large band gap energy blue shift around 70 nm after intermixing. Measured two-photon absorption coefficients showed a significant polarization dependence and suppression of up to 80% after intermixing. Similar polarization dependencies and suppression were observed in three-photon absorption and nonlinear refraction. Advanced modeling of second-harmonic generation showed reductions of over 50% in efficiency due to linear losses alone. Self-phase modulation was found to be the dominant parasitic nonlinear effect on the conversion efficiency, with reductions of over 60%. Simulations of group velocity mismatch showed modest reductions in efficiency of less than 10%. Experiments on second-harmonic generation showed improvements in efficiency over previous generations due to low linear loss and improved intermixing. The improvements permitted demonstration of continuous wave second-harmonic generation for the first time in such structures with output power exceeding 1 µW. Also, Type-II phase matching was demonstrated for the first time. Saturation was observed as the power was increased, which, as predicted, was the result of self-phase modulation when using 2 ps pulses. By using 20 ps pulses instead, saturation effects were avoided. Thermo-optically induced bistability was observed in continuous wave experiments. Difference frequency generation was demonstrated with wavelengths from the optical C-band being converted to the L- and U-bands with continuous waves. Conversion for Type-I phase matching was demonstrated over 20 nm with signal and idler wavelengths being separated by over 100 nm. Type-II phase matched conversion was also observed. Using the experimental data for analysis, self-pumped conversion devices were found to require external amplification to reach practical output powers. Threshold pump powers for optical parametric oscillators were calculated to be impractically large. Proposed improvements to the device design are predicted to allow more practical operation of integrated conversion devices based on quasi-phase matching superlattice waveguides.

Boolean functions are accepted to be cryptographically strong if they satisfy some common pre-determined criteria. It is expected that any design criteria should remain invariant under a large group of transformations due to the theory of similarity of secrecy systems proposed by Shannon. One of the most important design criteria for cryptographically strong Boolean functions is the nonlinearity criterion. Meier and Staffelbach studied nonlinearity preserving transformations, by considering the invertible transformations acting on the arguments of Boolean functions, namely the pre-transformations. In this thesis, first, the results obtained by Meier and Staffelbach are presented. Then, the invertible transformations acting on the truth tables of Boolean functions, namely the post-transformations, are studied in order to determine whether they keep the nonlinearity criterion invariant. The equivalent counterparts of Meier and Staffelbach&rsquo / s results are obtained in terms of the post-transformations. In addition, the existence of nonlinearity preserving post-transformations, which are not equivalent to pre-transformations, is proved. The necessary and sufficient conditions for an affine post-transformation to preserve nonlinearity are proposed and proved. Moreover, the sufficient conditions for an non-affine post-transformation to keep nonlinearity invariant are proposed. Furthermore, it is proved that the smart hill climbing method, which is introduced to improve nonlinearity of Boolean functions by Millan et. al., is equivalent to applying a post-transformation to a single Boolean function. Finally, the necessary and sufficient condition for an affine pre-transformation to preserve the strict avalanche criterion is proposed and proved.

A Boolean function can be represented in several different forms. These different representation have advantages and disadvantages of their own. The Algebraic Normal Form, truth table, and Walsh spectrum representations are widely studied in literature. In 1999, Claude Carlet and Phillippe Guillot introduced the Numerical Normal Form. NumericalNormal Form(NNF) of a Boolean function is similar to Algebraic Normal Form, with integer coefficients instead of coefficients from the two element field. Using NNF representation, just like the Walsh spectrum, characterization of several cryptographically important functions, such as resilient and bent functions, is possible. In 2002, Carlet had shown several divisibility results concerning resilient and correlation-immune functions using NNF. With these divisibility results, Carlet is able to give bounds concerning nonlinearity of resilient and correlation immune functions. In this thesis, following Carlet and Guillot, we introduce the Numerical Normal Form and derive the pairwise relations between the mentioned representations. Characterization of Boolean, resilient and bent functions using NNF is also given. We then review the divisibility results of Carlet, which will be linked to some results on the nonlinearity of resilient and correlation immune functions. We show the M&ouml / bius inversion properties of NNF of a Boolean function, using Gian-Carlo Rota&rsquo / s work as a guide. Finally, using a lot of the mentioned results, we prove a necessary condition on theWalsh spectrum of Boolean functions with given degree.

In cryptography especially in block cipher design, Boolean functions are the basic elements. A cryptographic function should have high nonlinearity as it can be attacked by linear attack. In this thesis the highest possible nonlinear boolean functions in the even dimension, that is bent functions, basic properties and construction methods of bent functions are studied. Also normal bent functions and generalized bent functions are presented.

The objective of this research is to presents new acoustic echo cancellation design methods that can effectively work in the nonlinear environment. Acoustic echo is an annoying issue for voice communication systems. Because of room acoustics and delay in the transmission path, echoes affect the sound quality and may hamper communications. Acoustic echo cancellers (AECs) are employed to remove the acoustic echo while keeping full-duplex communications. AEC designs face a variety of challenges, including long room impulse response, acoustic path nonlinearity, ambient noise, and double-talk situation. We investigate two parts of echo canceller design: echo cancellation algorithm design and control logic algorithm design. In the first part, our work focuses on the nonlinear adaptive and fast-convergence algorithms. We investigate three different structures: predistortion linearization, cascade structure, and nonlinear residual echo suppressor. Specifically, we are interested in the coherence function, since it provides a means for quantifying linear association between two stationary random processes. By using the coherence as a criterion to design the nonlinear echo canceller in the system, our method guarantees the algorithm stability and leads to a faster convergence rate. In the second part, our work focuses on the robustness of AECs in the presence of interference. With regard to the near-end speech, we investigate the double-talk detector (DTD) design in conjunction with nonlinear AECs. Specifically, we propose to design a DTD based on the mutual information (MI). We show that the advantage of the MI-based method, when compared with the existing methods, is that it is applicable to both the linear and nonlinear scenarios. With respect to the background noise, we propose a variable step-size and variable tap-length least mean square (LMS) algorithm. Based on the fact that the room impulse response usually exhibits an exponential decay power profile in acoustic echo cancellation applications, the proposed method finds optimal step size and tap length at each iteration. Thus, it achieves faster convergence rate and better steady-state performance. We show a number of experimental results to illustrate the performance of the proposed algorithms.

The aim of the research presented in this thesis is to investigate the use of various optimisation heuristics in the fields of automated cryptanalysis and automated cryptographic function generation. These techniques were found to provide a successful method of automated cryptanalysis of a variety of the classical ciphers. Also, they were found to enhance existing fast correlation attacks on certain stream ciphers. A previously proposed attack of the knapsack cipher is shown to be flawed due to the absence of a suitable solution evaluation mechanism. Finally, a new approach for finding highly nonlinear Boolean functions is introduced.

La modélisation numérique des structures composites à renfort fibreux de géométrie complexe constitue un axe de recherche majeur afin de prédire correctement leur comportement mécanique. Dans ce contexte, l’étude menée dans ce travail de thèse porte sur le développement de nouveaux éléments finis basés sur une approche numérique multi-échelle, appelée Approche de la Fibre Projetée (AFP). Cette approche a l’avantage de tenir compte de la présence des fibres au sein d’un espace matrice sans les discrétiser, ce qui limite considérablement la taille du système à résoudre. Pour analyser le comportement des structures composites, plusieurs éléments finis 2D et 3D ont été développés et implémentés dans le code ABAQUS via la routine UEL. Plusieurs cas tests de validation sont considérés pour tester la précision et l’efficacité des éléments finis proposés et les résultats obtenus sont globalement en bon accord avec les solutions de référence. De plus, l’intérêt de la nouvelle approche (AFP) est particulièrement mis en exergue en étudiant des structures composites complexe à renfort 3D : une plaque sandwich cousue et une plaque sandwich à âme creuse renforcée par des fibres en forme de « 8 ». / Numerical modeling of composite materials and structures with complex geometry of fiber reinforcement, such as stitched composites, constitutes a major research axis in order to correctly predict their mechanical behavior. Within this context, this study focuses on the development of new linear and nonlinear specific finite elements based on a multiscale numerical approach, called the Projected Fiber Approach (PFA). This numerical approach has the advantage of taking into account the presence of fi bers, long or short and distributed randomly or specifically, within a matrix space without discretizing them. Consequently, the obtained system of equations size is equivalent to that without reinforcement (matrix), which considerably reduces the computational cost. To analyze the linear and geometrically nonlinear behaviors of composite structures, two membrane finite elements, named PFT3 and PFQ4, and a 3D solid finite element, named PFH8, were developed and implemented into the commercial finite element code ABAQUS via the user element subroutine (UEL). Several numerical linear and nonlinear tests are considered to assess the accuracy and efficiency of the proposed composite finite elements, and the obtained results are globally in good agreement with the reference solutions. Moreover, the major interest of the PFA approach is particularly emphasized by studying two 3D complex reinforced composite structures: a stitched sandwich plate and a hollow core sandwich plate reinforced by "8" shape fibers.

[pt] O objetivo deste trabalho é complementar a ferramenta de dimensionamento de pórticos planos de concreto armado já existente no Ftool, programa educacional amplamente difundido no meio acadêmico. Para tanto, foi introduzido o cálculo e dimensionamento de pilares de concreto armado à flexão composta reta. Foi adicionada uma nova seção transversal, referente aos pilares retangulares com armaduras simétricas. Além disso, foi necessária a inclusão de um método de análise não linear geométrica simplificado que fosse compatível com a filosofia do Ftool, aliando simplicidade e eficiência: o método dos Dois Ciclos Iterativos. A ferramenta para análise não linear geométrica pode ou não ser utilizada em conjunto com a ferramenta para o dimensionamento de estruturas de concreto armado, sendo possível a análise não linear geométrica de pórticos planos constituídos de outros materiais. A metodologia utilizada para o dimensionamento dos pilares em concreto armado é a que se baseia nas zonas de solicitação e foi adequada para estar de acordo com a norma brasileira vigente, a ABNT NBR 6118:2014, assim como o dimensionamento de vigas existente em uma versão anterior dessa ferramenta. Dessa forma, é possível exibir resultados para pórticos planos compostos por vigas e pilares em concreto armado, nos mesmos moldes da versão anterior, com diagramas para as armaduras longitudinal e transversal disponíveis nos modos necessária e adotada. / [en] The main objective of this work is to complement the reinforced concrete plane frames design tool already existing in Ftool, an educational tool widely known in academia. Therefore, the design of reinforced concrete columns was introduced. A new cross section for rectangular columns with symmetrical steel reinforcement was added. In addition to that, the inclusion of a simplified nonlinear geometric analysis that was in accordance to the philosophy of Ftool, combining simplicity and efficiency, was needed: the Two cycles iterative method. The nonlinear geometric analysis tool may or may not be used together with the reinforced concrete plane frames design tool, thus allowing for geometric nonlinear analyses of plane frames of other materials. The methodology used for the reinforced concrete frames design was based on solicitation zones and was adapted to be in accordance with the Brazilian code, the ABNT NBR 6118:2014, as was the existing reinforced concrete beams design tool. It is now possible to show results for plane frames composed of reinforced concrete columns and beams just as in the previous version of the reinforced concrete design tool, showing diagrams for the necessary and adopted longitudinal and transversal steel reinforcement.

Les structures sandwichs sont largement utilisées dans le domaine de l’aéronautique et de l’espace du fait de leur bon rapport rigidité sur masse. Cependant, leur amortissement doit être amélioré pour le confort des utilisateurs et la durabilité des structures. L’objectif de cette thèse est d’étudier l’amortissement apporté à une structure sandwich par l’utilisation d’un matériau d’âme récemment développé. Ce matériau est fabriqué à base de fibres de carbone enchevêtrées, réticulées avec de la résine époxy. Le matériau enchevêtré-Réticulé est d’abord étudié seul. Les mesures expérimentales montrent un comportement dépendant de l’amplitude et de l’historique de sollicitation, et indépendant de la fréquence. Un modèle d’hystérésis est développé pour décrire les boucles contrainte-Déformation mesurées. L’étude théorique d’une structure à un degré de liberté permet de détailler l’effet des différentes composantes de ces boucles sur la réponse dynamique. Le matériau est ensuite inclus dans une poutre sandwich. Un modèle de vibrations de poutres sandwichs en flexion est proposé pour inclure un comportement non-Linéaire dissipatif du matériau d’âme. Une étude expérimentale est menée sur des poutres sandwichs, montrant un amortissement très supérieur à celui apporté par un matériau d’âme classique comme le nid d’abeille. Les simulations réalisées avec le modèle de poutre sandwich et le modèle d’hystérésis permettent de bien capturer les phénomènes non-Linéaires observés. A la fin de l’étude, une utilisation mixte d’un matériau d’âme en nid d’abeille et d’un matériau d’âme enchevêtré-Réticulé est proposée afin d’obtenir un bon amortissement pour un faible ajout de masse. / Sandwich structures are widely used in aerospace applications for their very good stiffness to weight properties. However, the damping properties of these structures have to be improved for user comfort and structural durability. The aim of this thesis is to study how the use of a recently developped core material can increase damping in sandwich structures. This material is made with entangled carbon fibres cross-Linked with epoxy resin. The entangled-Cross-Linked material is first studied separately. Experimental measurements show that the behavior depends strongly on strain amplitude and excitation history, while it depends weakly on frequency. A hysteresis model is developed to describe measured stress-Strain loops. A single-Degree-Of-Freedom structure containing the material is studied theoretically to show the effect of the different parts of the hysteresis loops on the steadystateand transient responses. The material is then included in a sandwich beam. A model for the bending vibrations of a sandwich beam is developped to include any nonlinear nonconservative behavior of the core material. Sandwich beams are then studied experimentally, showing a much higher damping than for classical core materials such as honeycomb. Simulations made with the sandwich beam model and the hysteresis loop model capture well the observed nonlinear phenomena. At the end of the study, a mixed use of honeycomb and entangled-Cross-Linked core materials is proposed, in order to obtain a high level of damping without adding much weight to the structure.