L’enrichissement des éléments finis standard est un outil performant pour améliorer la qualité d’approximation. L’idée principale de cette approche est d’ajouter aux fonctions de base un ensemble de fonctions censées améliorer la qualité des solutions approchées. Le choix de ces dernières est crucial et est en grande partie basé sur la connaissance a priori de quelques informations telles que les caractéristiques de la solution, de la géométrie du problème à résoudre, etc. L’efficacité de cette approche pour résoudre une équation aux dérivées partielles dans un maillage fixe, sans avoir recours au raffinement, a été prouvée dans de nombreuses applications dans la littérature. La clé de son succès repose principalement sur le bon choix des fonctions de base et plus particulièrement celui des fonctions d’enrichissement. Une question importante se pose alors : quelles conditions faut-il imposer sur les fonctions d’enrichissement afin qu’elles génèrent des éléments finis bien définis ?Dans cette thèse sont abordés différents aspects d’une approche générale d’enrichissement d’éléments finis. Notre première contribution porte principalement sur l’enrichissement de l’élément fini du type Q_1. Par contre, notre seconde contribution, certainement la plus importante, met l’accent sur une approche plus générale pour enrichir n’importe quel élément fini qu’il soit P_k, Q_k ou autres, conformes ou non conformes. Cette approche a conduit à l’obtention des versions enrichies de l’élément de Han, l’élément de Rannacher-Turek et l’élément de Wilson, qui font maintenant partie des codes d’éléments finis les plus couramment utilisés en milieu industriel. Pour établir ces extensions, nous avons eu recours à l’élaboration de nouvelles formules de quadrature multidimensionnelles appropriées généralisant les formules classiques bien connues en dimension 1, dites du “point milieu,” des “trapèzes” et de leurs versions perturbées, ainsi que la formule de Simpson. Elles peuvent être vues comme des extensions naturelles de ces formules en dimension supérieure. Ces dernières, en plus de leurs tests numériques implémentés sous MATLAB, version R2016a, ont fait l’objet de notre troisième contribution. Nous mettons particulièrement l’accent sur la détermination explicite des meilleures constantes possibles apparaissant dans les estimations d’erreur pour ces formules d’intégration. Enfin, dans la quatrième contribution nous testons notre approche pour résoudre numériquement le problème d’élasticité linéaire à l’aide d’un maillage rectangulaire. Nous effectuons l’analyse numérique aussi bien l’analyse de l’erreur d’approximation et résultats de convergence que l’analyse de l’erreur de consistance. Nous montrons également comment cette dernière peut être établie à n’importe quel ordre, généralisant ainsi certains travaux menés dans le domaine. Nous réalisons la mise en œuvre de la méthode et donnons quelques résultats numériques établis à l’aide de la bibliothèque libre d’éléments finis GetFEM++, version 5.0. Le but principal de cette partie sert aussi bien à la validation de nos résultats théoriques, qu’à montrer comment notre approche permet d’élargir la gamme de choix des fonctions d’enrichissement. En outre, elle permet de montrer comment cette large gamme de choix peut aider à avoir des solutions optimales et également à améliorer la validité et la qualité de l’espace d’approximation enrichie. / The enrichment of standard finite elements is a powerful tool to improve the quality of approximation. The main idea of this approach is to incorporate some additional functions on the set of basis functions. These latter are requested to improve the accuracy of the approximate solution. Their best choice is crucial and is based on the knowledge of some a priori information, such as the characteristics of the solution, the geometry of the problem to be solved, etc. The efficiency of such an approach for finding numerical solutions of partial differential equations using a fixed mesh, without recourse to refinement, was proved in numerous applications in the literature. However, the key to its success lies mainly on the best choice of the basis functions, and more particularly those of enrichment functions.An important question then arises: How to suitably choose them, in such a way that they generate a well-defined finite element ?In this thesis, we present a general approach that enables an enrichment of the finite element approximation. This was the subject of our first contribution, which was devoted to the enrichment of the classical Q_1 element, as a first step. As a second step, in our second contribution, we have developed a more general framework for enriching any finite element either P_k, Q_k or others, conforming or nonconforming. As an illustration of how to use this framework to build new enriched finite elements, we have introduced the extensions of some well-known nonconforming finite elements, notably, Han element, Rannacher-Turek element and Wilson element, which are now part of the main code of finite element methods. To establish these extensions, we have introduced a new family of multivariate versions of the classical trapezoidal, midpoint and Simpson rules. These latter, in addition to their numerical tests under MATLAB, version R2016a, have been the subject of our third contribution. They may be viewed as an extension of the well-known trapezoidal, midpoint and Simpson’s one-dimensional rules to higher dimensions. We particularly pay attention to the explicit expressions of the best possible constants appearing in the error estimates for these cubatute formulas. Finally, in the fourth contribution we apply our approach to numerically solving the linear elasticity problem based on a rectangular mesh. We carry out the numerical analysis of the approximation error and also for the consistency error, and show how the latter can be established to any order. This constitutes a generalization of some work already done in the field. In addition to our theoretical results, we have also made some numerical tests, which were achieved by using the GetFEM++ library, version 5.0. The aim of this contribution was not only to confirm our theoretical predictions, but also to show how the new developed framework allows us to expand the range of choices of enrichment functions. Furthermore, we have shown how this wide choices range can help us to improve some approximation properties and to get the optimal solutions for the particular problem of elasticity.

The system diagrams for the digital radio compatible with NASA's S-Band Space Network operating from 2025.8 - 2117.9 MHz (forward link) to 2200 - 2300 MHz (return link) are presented. The digital radio implementation includes binary phase shift keying (BPSK), quadrature phase shift keying (QPSK) and staggered quadrature phase shift keying (SQPSK). We have derived the system requirements for these modulation schemes from the Space Network User Guide (SNUG) and thereafter, derived system diagrams for the communication links. The designed system diagrams for the transceiver were implemented using Simulink models and USRP2 platform.

Les milieux biologiques sont des mélanges chimiques d'un intérêt exceptionnel. Leur étude nécessite la conception d'outils analytiques respectant les caractéristiques singulières et contraignantes de ces milieux. Nous avons développé un protocole d'imagerie non-invasif permettant de détecter sélectivement et de quantifier une espèce cible dans un mélange complexe telle qu'une cellule vivante. Notre approche exploite la réponse au premier ordre en quadrature de phase d'une sonde photochrome soumise à une modulation lumineuse périodique. Un cadre théorique complet nous a permis d'identifier les conditions d'illumination qui maximisent cette réponse en ajustant les deux paramètres de contrôle, l'intensité lumineuse moyenne et la fréquence angulaire de l'excitation lumineuse modulée, de sorte à satisfaire des conditions de résonance robustes. La contribution spécifique de la sonde photochrome ciblée au sein d'un mélange de composés interférents (photochromes ou non) est sélectivement extraite du signal global grâce à une détection en quadrature de phase. Après une validation in vitro, ce protocole a été appliqué en microscopie de fluorescence pour l'imagerie sélective dans des cellules de mammifères et des poissons zèbres. Cette approche ouvre des perspectives pour l'observation multiplexée dans des échantillons biologiques. Des améliorations ont été apportées au protocole original afin d'atteindre une résolution temporelle suffisante pour la plupart des études dynamiques en biologie. / Biological media are chemical mixtures of exceptional interest. Their investigation requires conceiving analytical tools fulfilling the singular and demanding features of these media. We have designed a non-invasive imaging protocol allowing to selectively detect and quantify a given target in a complex mixture such as a living cell. Our approach relies on the first order out-of-phase response of a targeted photoswitchable probe to periodic light modulation. An extensive theoretical framework enabled us to identify the illumination conditions that maximize this response by appropriately tuning the two control parameters, the average light intensity and the radial frequency of the modulated light excitation, so as to satisfy robust resonance conditions. The specific contribution of the targeted probe within a mixture of interfering species (photoswitchable or not) is selectively retrieved from the overall signal thanks to quadrature detection. After in vitro validation, this protocol was applied in optical fluorescence microscopy for selective imaging in mammalian cells and zebrafish. This approach opens attractive perspectives for multiplexed observations in biological samples. Further refinements allowed to reach a temporal resolution relevant for most dynamic studies in biology.

ITC/USA 2008 Conference Proceedings / The Forty-Fourth Annual International Telemetering Conference and Technical Exhibition / October 27-30, 2008 / Town and Country Resort & Convention Center, San Diego, California / This paper describes the use of orthogonal space-time block codes to overcome the performance and complexity difficulties associated with the use of Shaped Offset QPSK (SOQPSK) modulation, a ternary continuous phase modulation (CPM), in multiple-input multiple-output telemetry systems. The orthogonal space-time block code is applied to SOQPSK waveforms in the same way it would be applied to symbols. The procedure allows the receiver to orthogonalize the link. The main benefits of this orthogonalization are the easy realization of the transmit diversity for the offset-featured SQOSPK, and the removal of the noise correlation at the input to the space-time decoder and the elimination of I/Q interference when space time orthogonalization is applied to the symbol level.

International Telemetering Conference Proceedings / October 25-28, 1999 / Riviera Hotel and Convention Center, Las Vegas, Nevada / An all-digital high data rate parallel receiver architecture developed jointly by Goddard Space Flight Center and the Jet Propulsion Laboratory is pre- sented. This receiver utilizes only a small number of high speed components along with a majority of lower speed components operating in a parallel fre- quency domain structure implementable in CMOS, and can process over 600 Mbps with numerous varieties of QPSK modulation, including those incorpo- rating precise pulse shaping for bandwidth eÆcient modulation. Performance results for this receiver for bandwidth eÆcient QPSK modulation schemes such as square-root raised cosine pulse shaped QPSK and Feher’s patented QPSK are presented, demonstrating the great degree of exibility and high performance of the receiver architecture.

International Telemetering Conference Proceedings / October 26-29, 1998 / Town & Country Resort Hotel and Convention Center, San Diego, California / A new constant envelope modulation scheme and architecture for QPSK by cubic spline interpolation methods which increase spectral efficiency and power efficiency, named FQPSK-L, is presented. This modulation technique is an extension of the Feher Quadrature Shift Keying (FQPSK) patented technologies, see Ref [1]. Being a constant envelope modulation, FQPSK-L can operate with class C power amplifier without spectrum regrowth. We achieve a more compact spectrum with comparable bit error rate performance. For example, FQPSK-L is about 20% more spectral efficient than GMSK BTb=0.3 from 40 to 70 dB attenuation point. Moreover, FQPSK-L intrinsically has spikes at fc ± 0.5fb, fc ± 1.0fb, fc ± 1.5fb, ... which are useful for carrier recovery, symbol time recovery and fading compensation. In Rayleigh fading channel, FQPSK-L outperform GMSK BTb=0.3 by 0.8 dB. FQPSK-L is an excellent scheme for wireless and satellite communications which require high spectral and power efficiency.

International Telemetering Conference Proceedings / October 27-30, 1997 / Riviera Hotel and Convention Center, Las Vegas, Nevada / The aeronautical telemetry community is investigating alternative modulation methods to the commonly used non-return-to-zero (NRZ) pulse code modulation (PCM)/frequency modulation (FM). This paper outlines the important characteristics being investigated. Measured data comparing the spectral occupancy and bit error probability (BEP) performance of PCM/FM with that of a prototype constant envelope Feher’s quadrature phase shift keying (FQPSK) modulator and demodulator will also be presented. Measured results in several radio frequency bands demonstrate that the 99.99% and -60 dBc bandwidths of filtered FQPSK are only approximately one-half of the corresponding bandwidths of optimized PCM/FM even when the signal is non-linearly amplified. The signal energy per bit to noise power spectral density (E /N ) required for a BEP of 1×10 b 0 -5 for non-optimized FQPSK was approximately 12 dB which is approximately the same as limiter discriminator detected PCM/FM.

International Telemetering Conference Proceedings / October 23-26, 2000 / Town & Country Hotel and Conference Center, San Diego, California / Design and performance evaluation of a low-complexity equalizer for recently standardized spectral efficient Feher patented quadrature phase shift keying (FQPSK) system [1] over multipath fading channel is presented. The implementation based on a Feher patented equalizer (FE) [1] is of a structure with three branches, which are individually used to compensate for a moving fade notch with different locations. These branches are switched by the control signal that is generated based on pseudo-error on-line detection technique. It is demonstrated that for typical aeronautical telemetry RF frequency selective fading channels, having delay spreads in 20 – 200 ns range, the adaptive FE reduces the number of statistical outages by more than 60% without the need for training bits and without increasing the receiver synchronization time.

This thesis consists of three papers, all treating various aspects of the operation partial balayage from potential theory. The first paper concerns the equilibrium measure in the setting of two dimensional weighted potential theory, an important measure arising in various mathematical areas, e.g. random matrix theory and the theory of orthogonal polynomials. In this paper we show that the equilibrium measure satisfies a complementary relation with a partial balayage measure if the weight function is of a certain type. The second paper treats the connection between partial balayage measures and measures arising from scaling limits of a generalisation of the so-called divisible sandpile model on lattices. The standard divisible sandpile can, in a natural way, be considered a discrete version of the partial balayage operation with respect to the Lebesgue measure. The generalisation that is developed in this paper is essentially a discrete version of the partial balayage operation with respect to more general measures than the Lebesgue measure. In the third paper we develop a version of partial balayage on Riemannian manifolds, using the theory of currents. Several known properties of partial balayage measures are shown to have corresponding results in the Riemannian manifold setting, one of which being the main result of the first paper. Moreover, we utilize the developed framework to show that for manifolds of dimension two, harmonic and geodesic balls are locally equivalent if and only if the manifold locally has constant curvature. / Denna avhandling består av tre artiklar som alla behandlar olika aspekter av den potentialteoretiska operationen partiell balayage. Den första artikeln betraktar jämviktsmåttet i tvådimensionell viktad potentialteori, ett viktigt mått inom flertalet matematiska inriktningar såsom slumpmatristeori och teorin om ortogonalpolynom. I denna artikel visas att jämviktsmåttet uppfyller en komplementaritetsrelation med ett partiell balayage-mått om viktfunktionen är av en viss typ. Den andra artikeln behandlar relationen mellan partiell balayage-mått och mått som uppstår från skalningsgränser av en generalisering av den så kallade "delbara sandhögen", en diskret modell för partikelaggregation på gitter. Den vanliga delbara sandhögen kan på ett naturligt sätt betraktas som en diskret version av partiell balayage-operatorn med avseende på Lebesguemåttet. Generaliseringen som utarbetas i denna artikel är väsentligen en diskret version av partiell balayage-operatorn med avseende på mer allmänna mått än Lebesguemåttet. I den tredje artikeln formuleras en version av partiell balayage på riemannska mångfalder utifrån teorin om strömmar. Åtskilliga tidigare kända egenskaper om partiella balayage-mått visas ha motsvarande formuleringar i formuleringen på riemannska mångfalder, bland annat huvudresultatet från den första artikeln. Vidare så utnyttjas det utarbetade ramverket för att visa att tvådimensionella riemannska mångfalder har egenskapen att harmoniska och geodetiska bollar lokalt är ekvivalenta om och endast om mångfalden lokalt har konstant krökning. / <p>QC 20160524</p>

International Telemetering Conference Proceedings / October 25-28, 1999 / Riviera Hotel and Convention Center, Las Vegas, Nevada / This paper describes the design considerations used by Aydin Telemetry in the development of its high data rate Feher Patented Quadrature Phase Shift Keying (FQPSK) [1] frequency agile transmitter. We will address several key areas of interest to the Telemetry community, such as the use of commercially available VLSI parts to minimize parts count while maximizing reliability, adaptive filtering to accommodate a wide range of data rates, and user selectable features to achieve a universal transmitter design. User selectable features include differential encoder, 15 stage IRIG randomizer, and 1/2 rate convolutional FEC coding. This paper also addresses the spectral efficiency that can be achieved using a Class-C amplifier with FQPSK and the measured bit error rate (BER) performance versus Eb/No.