Cette thèse s'inscrit dans la thématique de l'étude de la formation et de l'évolution des systèmes planétaire grâce à la méthode de l'imagerie à haut contraste, aussi appelée imagerie directe, par comparaison aux méthodes de détection dites "indirectes". Le travail que je présente dans ce manuscrit s'articule en deux parties bien distinctes. La première partie concerne la composante observationnel de ma thèse, à l'aide de l'instrument SPHERE installé au Very Large Telescope, au sein du consortium du même nom. L'instrument SPHERE a pour objectif la détection et la caractérisation de jeunes et massives exoplanètes mais également de disques circumstellaires allant des très jeune disques protoplanétaires aux disques de débris, plus âgés. Ainsi, je présente dans ce manuscrit ma contribution au programme SHINE, un grand relevé de 200 nuits dont le but est la détection de nouvelles exoplanètes ainsi que la caractérisation spectrale et orbitale des quelques compagnons déjà connus. J'y présente également les deux études de disques circumstellaires que j'ai réalisées, autour des étoiles HD 141569 et HIP 86598. La première étude ayant permis la découverte d'anneaux concentriques à quelques dizaine d'UA de l'étoile ainsi que de asymétrie dans le flux du disque inhabituelle. La seconde étude porte sur la découverte d'un disque de débris présentant également une asymétrie en flux inhabituelle. La deuxième partie concerne la composante instrumentale de mon travail de thèse, au sein du consortium MICADO, en charge de la conception de la caméra du même nom qui sera l'un des instruments de première lumière de l'Extremely Large Telescope Européen (ELT). Dans ce manuscrit, je présente l'étude que j'ai menée afin de définir le design de certain composant du mode coronographique de MICADO tout en tenant compte des contraintes de l'instrument qui n'est pas dédié à l'imagerie haut contraste, contrairement à SPHERE. / This thesis is performed in the context of the study of the formation and evolution of planetary systems using high contrast imaging, also known as direct imaging in contrast to so-called "indirect" detection methods. The work I present in this manuscript is divided into two distinct parts.The first part concerns the observational component of my thesis, using the SPHERE instrument installed at Very LargeTelescope. This work was done as part of the consortium of the same name. The purpose of the SPHERE instrument is to detect and characterize young and massive exoplanets, but also circumstellar disks ranging from very young protoplanetary disks to older debris disks. In this manuscript, I present my contribution to the program SHINE, a large survey with an integration time of 200 nights' worth of observation, the goal of which is the detection of new exoplanets and the spectral and orbital characterization of some previously-known companions. I also present the two studies of circumstellar disks that I made, around the stars HD 141569 and HIP 86598. The first study allowed the discovery of concentric rings at about ten AU of the star along with an unusual flux asymmetry in the disk. The second study is about the discovery of a debris disk that also has an unusual flux asymmetry. The second part concerns the instrumental component of my thesis work done within the MICADO consortium, in charge of the design of the camera of the same name which will be one of the first light instruments of the European Extremely Large Telescope (ELT). In this manuscript, I present the study in which I define the design of some components of the coronagraphic mode of MICADO while taking into account the constraints of the instrument - which is not dedicated to high contrast imaging, unlike SPHERE.

The viability of using a slicer based integral field spectrograph (IFS) for high contrast observations has been under scrutiny due to the belief that the one dimensional coherence that persists along the slice to the point of sampling at the detector will cause the creation of secondary speckles that will not have the same characteristics as normal speckles, thus stopping us from calibrating them out. It has also been previously assumed that a suitably low differential wavefront error when moving slice to slice was not guaranteed by design. It was for these reasons that slicer based IFSs were not selected for the current generation of planet finding instruments. As part of the EPICS (Exo Planet Imaging Camera and Spectrograph for the E-ELT) design study it was decided that slicers should be re-investigated due to results from on sky observations suggesting these limitations did not exist. The purpose of this thesis was to determine whether there was validity to the concerns mentioned above and therefore to answer the question; Would implementing a slicer based integral field spectrograph limit the achievable contrast of an instrument designed for the direct detection of exoplanets? Chapter 1 gives a brief introduction into the field of exoplanet research. Charpter 2 describes the noise limiting direct detection of exoplanets and the ways to get around it. Chapter 3 gives an overview of the two types of IFS under investigation by the EPICS consortium. Chapter 4 looks into details of the EPICS instrument and the IFS design study that came about. Chapter 5 shows simulations performed for the aim of achieving better contrasts via post processing methods and accurate data reduction as well as simulations of slicer based integral field spectrographs. Experimental tests using a slicer and a preoptics setup designed to simulate the limiting noise are described in Chapter 6. Chapter 7 looks at using SINFONI for high contrast observations and Chapter 8 details the conclusions drawn from the work presented in this thesis, as well as possible extensions to it. The work performed in this thesis dispels the concerns about the continued one dimensional coherence up to the detecter and suggests that slicer based integral field spectrographs do not inherently limit the contrast achievable; Results from experiments fit well with the requirements for EPICS to achieve its goals. Simulations also supported the idea that secondary speckle noise should not be an issue for the slicer based IFS. This means that a slicer based IFS is a viable option for the EPICS instrument.

Flows, instabilities, and magnetism play significant roles in the internal and atmospheric dynamics of objects ranging from the smallest exoplanets to the largest stars. These phenomena are governed by the equations of magnetohydrodynamics (MHD), which link the flows and magnetic fields, and from which the operational parameters and growth rates of instabilities can be recovered. Here we present an overview of interesting phenomena (such as the internal dynamics of stellar and planetary objects, as well as instabilities which might operate within these environs), as well as computational techniques by which these phenomena might both be understood and analysed (through both ‘simplifications’ of the MHD equations and different numerical/computational approaches). We first present an investigation into the Heat-Flux-Driven Buoyancy Instability (HBI) within stellar and planetary atmospheres, considering both the parameter space it might operate within as well as its non-linear effects during said operation. We find that whilst the HBI may be able to play a role in Solar, stellar and planetary atmospheres, it is likely to be quite limited in scope, only operating within small regions. However, its dramatic consequences for heat transport in the non-linearly evolved state, and the prospects that it may operate outside the narrow regimes that our analytical analysis suggested, suggest that it may merit further study. This is followed with a discussion of a method by which the surface flows of exoplanets might be measured: The Rossiter-Mclaughlin Effect at Secondary Eclipse (RMse). We formulate the effect, showing that the formalism is identical to the traditional Rossiter-Mclaughlin effect, albeit in a different frame (a planet transiting a star becomes a star transiting a planet), and consider its observational implications: the effect should be observable for the brightest planet hosting stars using upcoming 40m-class telescopes (i.e.E-ELT). We finish with a series of 3D anelastic simulations of fully convective stars, designed to investigate how the internal flows are affected by varying stellar parameters, as well as a possible link between residual entropy and differential rotation contours, and a method by which this link can be used (via the thermal wind equation - TWE) to extrapolate the internal rotation. We find a clear transition between ‘solar-like’ and ‘anti-solar’ internal dynamics, characterised in the meridional circulation, differential rotation, residual entropy, and angular momentum flux profiles. Furthermore we find that, whilst the alignment between residual entropy and differential rotation contours is somewhat varied, the resultant extrapolation, via the TWE, produces a generally good fit to the differential rotation contours, suggesting a general robustness to the theory.

Exoplanet discovery has grown more quickly in recent years. However, the nature of their discovery leaves many unanswered in questions regarding exoplanetary habitability. Proxima Centauri b, an exoplanet which orbits the Sun's closest stellar neighbour, Proxima Centauri, was recently discovered with a subzero equilibrium temperature. Although not considered habitable based on the classical definition of the liquid water range, there may be fractions of Proxima Centauri b which are habitable. A prior study simulated the climate conditions of Proxima Centauri b until equilibrium was reached, using a variety of initial conditions. In this project, various metrics for calculating the fractional habitability of Proxima Centauri b are presented and applied to the results of the prior study's simulations. Colormaps are used to show the ice and temperature distributions that produce the calculated values of fractional habitability. The fractional habitabilities calculated show that while the value is both case and metric dependent, for the vast majority of all cases and metrics the value is nonzero implying that Proxima Centauri b is likely to have habitable regions. / Upptäckandet av exoplaneter har ökat i takt över de senaste åren. Samtidigt, på grund av sättet som de upptäcks finns många obesvarade frågor angående planeternas beboelighet. Proxima Centauri b är en exoplanet som kretsar kring solens närmsta granne, Proxima Centauri. Exoplaneten upptäcktes nyligen med en jämviktstemperatur under $0\degree$C. Trots att exoplaneten inte anses beboelig enligt klassisk definition kan det finnas delar av Proxima Centauri b som är beboeliga. En tidigare studie simulerade klimatförhållandena av Proxima Centarui b till jämvikt nåddes, med varierade begynnelsetillstånd. I detta projekt beräknas andelen av Proxima Centauri b som är beboelig genom flera olika mått för "fractional habitability". Måtten jämförs med den tidigare studien och dess simuleringar. Grafiskt åsikdligörs resultaten via färgkartor över planeten för istjocklek och yttemperatur. De beräknade värdena på Proxima Centauri b's "fractional habitability" påvisar beroende på mått och begynnelsetillstånd. Däremot, för en majoritet av både fall och mått är värdet nollskilt vilket antyder att Proxima Centauri b är delvist beboelig.

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Les exoplanètes peuvent être détectées par plusieurs méthodes. De celles-ci, la méthode des Vitesses Radiales (RV) est dite indirecte, car l'on observe le spectre lumineux de l'étoile hôte et non la planète directement. Or, plusieurs facteurs influencent les variations lumineuses d'une étoile hormis la présence d'un compagnon. La photosphère des étoiles comprend des régions plus sombres appelées taches stellaires causées par de forts champs magnétiques qui restreignent le déplacement de l'énergie vers la surface. Lorsque l'étoile tourne, elles se déplacent produisant ainsi des variations dans le spectre de l'étoile similaires à celles induites par les corps l'orbitant. C'est pourquoi la modélisation de l'activité stellaire est essentielle pour la recherche d'exoplanètes. Il existe maints indicateurs d'activité dont la photométrie et les bissectrices et le Full Width at Half Maximum (FWHM) obtenus du profil moyen des raies spectrales. Ils peuvent être modélisés à l'aide d'outils mathématiques comme les Processus Gaussiens (GP). L'étoile GL229 A est une naine rouge située à 5.75 parsecs autour de laquelle orbite la première naine brune, GL229 B, découverte par imagerie directe en 1995. À mi-chemin entre planètes géantes et étoiles naines, ces objets sous-stellaires n'ont pas acquis la masse nécessaire pour déclencher la fusion nucléaire de l'hydrogène lors de leur formation. Le système GL229 fut aussi observé par différents télescopes dotés d'instruments permettant d'obtenir des mesures de RV. Ceci mena, en 2014 et 2020, à la détection de deux exoplanètes, GL229 A b et A c aux masses minimales de 32 et 7 masses terrestres. Ce mémoire présente une réanalyse des RV obtenues avec HARPS, un spectrographe échelle. En modélisant le FWHM avec un GP, il peut être démontré que les signaux précédemment identifiés comme d'origine planétaire correspondent en fait à des signaux d'activité stellaire. / Several methods can detect exoplanets. Of these, the Radial Velocity (RV) method is said to be indirect because the light spectrum of the host star is observed and not the planet directly. However, several factors influence a star's luminous variations apart from a companion's presence. The photosphere of stars contains darker regions called star spots caused by strong magnetic fields that restrict the movement of energy to the surface. When the star rotates, these spots move, producing variations in the star's spectrum similar to those induced by the bodies orbiting it. Hence, stellar modelling activity is essential when searching for exoplanets. Many activity indicators, including photometry and bisectors and Full Width at Half Maximum (FWHM) obtained from the average spectral line profiles, can be modelled using tools such as Gaussian Processes (GP). GL229 A is a red dwarf located at 5.75 parsecs around which orbits a brown dwarf, GL229 B, firstly discovered through direct imaging in 1995. Halfway between giant planets and dwarf stars, these substellar objects did not acquire the mass necessary to trigger nuclear hydrogen fusion during their formation. The GL229 system was also observed by various telescopes equipped with instruments making it possible to obtain RV measurements. This led, in 2014 and 2020, to the detection of two exoplanets, GL229 A b and A c, with minimum masses of 32 and 7 Earth masses. This thesis presents a re-analysis of the RVs obtained from HARPS spectra, an échelle spectrograph, for the Gliese 229 system. By modelling the FWHM with a GP, we show that previously identified planetary signals are not real and result from stellar activity.

L’objectif principal de cette thèse est de caractériser l’atmosphère de Jupiters chaudes par spectroscopie de transmission à haute résolution, dans l’infrarouge proche, avec l’instrument SPIRou. L’historique de formation, d’évolution et de migration des planètes est empreint dans leur composition chimique, et de retrouver cette composition permet d’en élucider le mystère. La spectroscopie de transit et d’émission a prouvé être fortement efficace à cette tâche, autant pour la détermination de la composition que pour la détermination d’autres caractéristiques atmosphériques comme le profil de température et la dynamique, accessibles à haute résolution. Les Jupiter Chaudes, planètes géantes gazeuses qui orbitent très près de leur étoile, offrent des conditions d’observations très favorables pour ce type d’étude. Encore beaucoup d’éléments nous échappent quant aux processus physiques, chimiques et dynamiques qui gouvernent l’atmosphère de ces objets astronomiques. Des études détaillées de ceux-ci, telles que celles présentées dans cette thèse, sont nécessaires pour mieux comprendre ces mécanismes. Dans un premier temps, nous avons fait l’étude de deux transits de HD 189733 b, une des exoplanètes les plus étudiées. Cela nous a permis de valider nos méthodes d’analyse avec des données provenant du spectropolarimètre infrarouge à haute résolution SPIRou, installé au télescope Canada-France-Hawaii, représentant d’ailleurs la première caractérisation d’une atmosphère en spectroscopie de transit pour le SPIRou Legacy Survey. Nous avons confirmé la présence d’un signal d’eau à un niveau de signification de plus de 5σ, basé sur les résultats de test-t. Nous présentons la première analyse de spectroscopie de transit haute résolution faite par méthode de récupération, basée sur l’inférence bayésienne et appliquée à une grille de modèles SCARLET interpolée. Celle-ci a permis d’inférer une abondance de log_10[H2O] ≃ −4.4. Les résultats obtenus sont cohérents avec la littérature et indiquent que l’atmosphère de HD 189733 b est relativement claire (sans nuages) et possède un C/O super-solaire (correspondant à une formation au-delà de la ligne de glace de l’eau). Un fort décalage vers le bleu de l’absorption par l’eau a été observé, indiquant la présence de forts vents allant du côté jour vers le côté nuit ou un signal dominé par le côté soir du terminateur (limbe arrière), ou une combinaison des deux. Dans un second temps, nous présentons la première analyse à haute résolution dans l’infrarouge proche de trois transits de la très peu dense sous-Saturne WASP-127 b. Une étude récente à basse résolution a montré un spectre de transmission riche et une abondance super-solaire de CO2 dans son atmosphère. La contribution de CO et de CO2 n’a cependant pu être démêlée étant donné la couverture spectrale et la résolution limitée des données HST et de Spitzer utilisées, menant à des scénarios équiprobables de faible et fort C/O. La couverture de la bande de CO à 2.3 μm par SPIRou a permis de faire cette différenciation, et nos résultats ont exclu la présence de CO en abondance supérieure à log_10[CO] = −4.3, impliquant que le signal détecté à 4.5μm dans les données Spitzer provient majoritairement du CO2. De plus, un calcul de test-t sur les données SPIRou a confirmé la détection de H2O à un niveau ajusté de 4.9σ, mais également une détection potentielle de OH, à 2.4σ. Cette présence extrêmement inattendue de OH pourrait potentiellement être expliquée si la température du côté jour est assez grande, aidée par l’irradiation amplifiée de l’étoile qui quitte la séquence principale, ou encore par du mélange vertical. Nous présentons également la première méthode de récupération complète appliquée à la spectroscopie de transit à haute résolution, en utilisant la suite de modèles petitRADTRANS, et sur trois ensembles de données différents : les données SPIRou, les données HST et Spitzer de l’étude initiale, et les deux ensembles de données combinés. Une comparaison des différents résultats obtenus confirme que l’analyse conjointe permet d’avoir de meilleures contraintes sur les paramètres atmosphériques. Alors que l’étude initiale favorisait un fort C/O, nos résultats pointent vers un C/O très sous-solaire, produit par un C/H sous-solaire et un O/H plutôt stellaire. Les scénarios de formation qui supportent une telle composition sont ceux au-delà des lignes de glace de H2O et de CO2 (∼ 10ua), avec une accrétion supplémentaire de matériel riche en O via la migration et le croisement des lignes de glaces. L’accrétion du matériel est soit dominée par le gaz et tardive (après 5 à 7 millions d’années), ou encore, mixte (de gaz et de glaces) et plus précoce, avec un mélange cœur-enveloppe substantiel. Bien qu’il en reste beaucoup à faire, ces travaux de recherche ont démontré que la spectroscopie de transit à haute résolution dans l’infrarouge proche est utile pour explorer les conditions atmosphériques des Jupiter et sous-Saturne chaudes, et plus spécifiquement, avec l’instrument SPIRou. La combinaison de données à faible et à haute résolution s’avère un outil très puissant pour l’étude des atmosphères, et le sera encore plus avec les capacités révolutionnaires de JWST. / The main objective of this thesis is to characterize the atmosphere of hot Jupiters with high resolution transmission spectroscopy in the near-infrared with the SPIRou instrument. The formation, evolution and migration history of exoplanets is imprinted in their chemical composition, and finding this composition makes it possible to trace back this history. Transit and emission spectroscopy have proven to be highly effective for this task, in the determination of the composition, but also of other atmospheric characteristics such as the temperature profile and the dynamics, accessible at high resolution. Hot Jupiters -- gas giant planets orbiting very close to their star -- offer highly favourable observation conditions for this type of study. Many pieces of the puzzle are still missing regarding the physical, chemical and dynamical processes that govern the atmospheres of these astronomical objects, and detailed studies, such as the ones presented in this thesis, are necessary to better understand those mechanisms. First, we present the results of our analysis of two HD189733b transits, one of the most studied exoplanets to date. This study allowed to validate our analysis method with SPIRou data, a high-resolution near-infrared spectro-polarimeter installed at the Canada-France-Hawaii Telescope. It also represents the first characterization of an atmosphere with transit spectroscopy as part of the SPIRou Legacy Survey. Our results confirmed the H2O detection in the planet's atmosphere at a 5 sigma level, based on a $t$-test. We present the first analysis of a Bayesian retrieval framework applied to high-resolution transmission spectroscopy, using a grid of SCARLET models. We constrained the H2O abundance to log_10[H2O] ~ -4.4$. The results are consistent with the literature and agree on the atmosphere of HD189733b being relatively clear (without clouds) and having a super-solar C/O (corresponding to a formation beyond the H2O ice line). A strong blue shift of the water absorption signal was observed, indicative of strong day-to-night winds or a signal dominated by the terminator's evening side (trailing limb), or a combination of both. Second, we present the first high-resolution analysis in the near-infrared of three transits of the super low-density sub-Saturn WASP-127b. A recent low-resolution study showed a rich transmission spectrum and super-solar abundance of CO2 in its atmosphere. However, the contribution of CO and CO2 could not be disentangled given the limited spectral coverage and resolution of the HST and Spitzer data, leading to equiprobable low and high C/O scenarios. The coverage of the CO band at 2.3um by SPIRou made it possible to differentiate between the two cases, and our results excluded CO abundances greater than 10^(-4.3), implying that the signal at 4.5um seen in the Spitzer data mostly comes from CO2. Moreover, a t-test analysis on the SPIRou data confirmed the detection of H2O at an adjusted level of 4.9 sigma, but also a tentative detection of OH, at 2.4 sigma. The presence of OH, although extremely unexpected, could potentially be explained from a high enough dayside temperature, increased by the amplified irradiation of the star leaving the main sequence, or from vertical mixing. We also present the first full-retrieval framework applied to transmission spectroscopy at high resolution, using the petitRADTRANS model suite on three different datasets: on the SPIRou data, on the HST and Spitzer data from the original study, and on both datasets combined. A comparison of the different results obtained confirms that the joint analysis provides better constraints on the atmospheric parameters. While the initial study favored a high C/O, our results point toward a highly subsolar C/O, produced by a sub-stellar C/H and a roughly stellar O/H. Formation scenarios that support such a composition are those beyond the H2O and CO2 ice lines (~ 10ua), with further accretion of O-rich material via migration and ice lines crossing. The primordial/bulk accretion was either gas-dominated and late (after 5-7 Myr), or earlier and mixed (with gas and ice), with substantial core-enveloppe mixing. Although much remains to be done, this research work has demonstrated that high-resolution near-infrared transit spectroscopy is useful for exploring the atmospheric conditions of hot Jupiters and sub-Saturns, and more specifically, with the SPIRou instrument. The combination of low and high resolution data has shown to be a very powerful tool for such studies, and will be even more so with the revolutionary capabilities of JWST.

This thesis is concerned with various aspects of the detection and characterisation of transiting extra-solar planets. The noise properties of photometric data from SuperWASP, a wide-field survey instrument designed to detect exoplanets, are investigated. There has been a large shortfall in the number of planets such transit surveys have detected, compared to previous predictions of the planet catch. It has been suggested that correlated, or red, noise in the photometry is responsible for this; here it is confirmed that red noise is present in the SuperWASP photometry, and its effects on planet discovery are quantified. Examples are given of follow-up photometry of candidate transiting planets, confirming that modestly-sized telescopes can rule out some candidates photometrically. A Markov-chain Monte Carlo code is developed to fit transit lightcurves and determine the depth of such lightcurves in different passbands. Tests of this code with transit data of WASP-3 b are reported. The results of a search for additional transiting planets in known transiting planetary systems are presented. SuperWASP photometry of 24 such systems is searched for additional transits. No further planets are discovered, but a strong periodic signal is detected in the photometry of WASP-10. This is ascribed to stellar rotational variation, the period of which is determined to be 11.91 ± 0.05 days. Monte Carlo modelling is performed to quantify the ability of SuperWASP to detect additional transiting planets; it is determined that there is a good (> 50 per cent) chance of detecting additional, Saturn-sized planets in P ~ 10 day orbits. Finally, the first-ever attempt to detect the secondary eclipse of a transiting extra-solar planet at radio wavelengths is made. Although no eclipse is conclusively detected, upper limits to the flux density from HD 189733 b are established, and compared to theoretical predictions of the flux due to electron-cyclotron maser emission.

I present the results of a comprehensive assessment of companions to 454 solar-type stars within 25 pc. New observational aspects of this work include surveys for (1) very close companions with long-baseline interferometry at the Center for High Angular Resolution Astronomy (CHARA) Array, (2) close companions with speckle interferometry, and (3) wide proper motion companions identified by blinking multi-epoch archival images. I have also obtained and included unpublished results from extensive radial velocity monitoring programs. The many sources utilized enable a thorough evaluation of stellar and brown dwarf companions. The results presented here include eight new companion discoveries, four of which are wide common proper motion pairs discovered by blinking archival images, and four more are from the spectroscopic data. The overall observed fractions of single, double, triple, and higher order systems are 57%±3%, 33%±2%, 8%±1%, and 3%±1%, respectively, counting all stellar and brown dwarf companions. The incompleteness analysis indicates that only a few undiscovered companions remain in this well-studied sample, showing that a majority of the solar-type stars are single. Bluer, more massive stars are more likely to have companions than redder, less massive ones. I confirm earlier expectations that more active stars are more likely to have companions. A preliminary, but important indication is that brown dwarfs, like planets, prefer stars with higher metallicity, tentatively suggesting that brown dwarfs may form like planets when they are companions to stars. The period distribution is unimodal and roughly Gaussian with peak and median values of about 300 years. The period-eccentricity relation shows a roughly flat distribution beyond the circularization limit of about 12 days. The mass-ratio distribution shows a clear discontinuity near a value of one, indicating a preference for twins, which are not confined to short orbital periods, suggesting that stars form by multiple formation mechanisms. The ratio of planet hosts among single, binary, and multiple systems are statistically indistinguishable, suggesting that planets are as likely to form around single stars as they are around components of binary or multiple systems at sufficiently wide separations.

Signal acquisition, signal reconstruction and analysis of spectrum of the signal are the three most important steps in signal processing and they are found in almost all of the modern day hardware. In most of the signal processing hardware, the signal of interest is sampled at uniform intervals satisfying some conditions like Nyquist rate. However, in some cases the privilege of having uniformly sampled data is lost due to some constraints on the hardware resources. In this thesis an important problem of signal reconstruction and spectral analysis from nonuniformly sampled data is addressed and a variety of methods are presented. The proposed methods are tested via numerical experiments on both artificial and real-life data sets. The thesis starts with a brief review of methods available in the literature for signal reconstruction and spectral analysis from non uniformly sampled data. The methods discussed in the thesis are classified into two broad categories - dense and sparse methods, the classification is based on the kind of spectra for which they are applicable. Under dense spectral methods the main contribution of the thesis is a non-parametric approach named LIMES, which recovers the smooth spectrum from non uniformly sampled data. Apart from recovering the spectrum, LIMES also gives an estimate of the covariance matrix. Under sparse methods the two main contributions are methods named SPICE and LIKES - both of them are user parameter free sparse estimation methods applicable for line spectral estimation. The other important contributions are extensions of SPICE and LIKES to multivariate time series and array processing models, and a solution to the grid selection problem in sparse estimation of spectral-line parameters. The third and final part of the thesis contains applications of the methods discussed in the thesis to the problem of radial velocity data analysis for exoplanet detection. Apart from the exoplanet application, an application based on Sudoku, which is related to sparse parameter estimation, is also discussed.