Constrained by practical and economical considerations, one often uses seismic data with missing traces. The use of such data results in image artifacts and poor spatial resolution. Sometimes due to practical limitations, measurements may be available on a perturbed grid, instead of on the designated grid. Due to algorithmic requirements, when such measurements are viewed as those on the designated grid, the recovery procedures may result in additional artifacts. This paper interpolates incomplete data onto regular grid via the Fourier domain, using a recently developed greedy algorithm. The basic objective is to study experimentally as to what could be the size of the perturbation in measurement coordinates that allows for the measurements on the perturbed grid to be considered as on the designated grid for faithful recovery. Our experimental work shows that for compressible signals, a uniformly distributed perturbation can be offset with slightly more number of measurements.

Η κωδικοποίηση στο χρόνο αποτελεί έναν πραγματικού-χρόνου, ασύγχρονο μηχανισμό κωδικοποίησης της πληροφορίας ενός αναλογικού σήματος πεπερασμένου εύρους ζώνης σε μία χρονική ακολουθία (χρονικά δείγματα), βάση της οποίας το σήμα μπορεί να ανακατασκευαστεί. Τα κυκλώματα τα οποία παράγουν αυτά τα χρονικά δείγματα και οι αλγόριθμοι οι οποίοι πραγματοποιούν την ανακατασκευή αναφέρονται ως Μηχανές Κωδικοποίησης στο Χρόνο (ΤΕΜs) και Μηχανές Αποκωδικοποίησης στο χρόνο (TDMs), αντίστοιχα. Αυτή η διαδικασία μπορεί να αντιμετωπιστεί ως ένας μηχανισμός δειγμaτοληψίας εξαρτώμενος από το σήμα και από τις παραμέτρους των παραπάνω κυκλωμάτων. Σε αυτήν τη διπλωματική εργασία, παρουσιάζουμε το θεωρητικό και μαθηματικό υπόβαθρο αυτής της καινοτόμας μεθόδου αναπαράστασης της πληροφορίας. / Time encoding is a real-time, asynchronous mechanism for encoding the information of an analog bandlimited signal into a time sequence (time samples) based on which the signal can be reconstructed. The circuits generating these time samples and the algorithms carrying out the reconstruction are referred to as Time Encoding Machines (TEMs) and Time Decoding Machines (TDMs), respectively. This procedure can be addressed as a sampling scheme which depends on the signal and the parameters of the above circuits. In this diploma thesis, we present the theoretical and mathematical framework of this innovative information representation procedure.

Compressed Sensing (CS) is a new paradigm in signal processing which exploits the sparse or compressible nature of the signal to significantly reduce the number of measurements, without compromising on the signal reconstruction quality. Recently, many algorithms have been reported in the literature for efficient sparse signal reconstruction. Nevertheless, it is well known that the performance of any sparse reconstruction algorithm depends on many parameters like number of measurements, dimension of the sparse signal, the level of sparsity, the measurement noise power, and the underlying statistical distribution of the non-zero elements of the signal. It has been observed that a satisfactory performance of the sparse reconstruction algorithm mandates certain requirement on these parameters, which is different for different algorithms. Many applications are unlikely to fulfil this requirement. For example, imaging speed is crucial in many Magnetic Resonance Imaging (MRI) applications. This restricts the number of measurements, which in turn affects the medical diagnosis using MRI. Hence, any strategy to improve the signal reconstruction in such adverse scenario is of substantial interest in CS. Interestingly, it can be observed that the performance degradation of the sparse recovery algorithms in the aforementioned cases does not always imply a complete failure. That is, even in such adverse situations, a sparse reconstruction algorithm may provide partially correct information about the signal. In this thesis, we study this scenario and propose a novel fusion framework and an iterative framework which exploit the partial information available in the sparse signal estimate(s) to improve sparse signal reconstruction. The proposed fusion framework employs multiple sparse reconstruction algorithms, independently, for signal reconstruction. We first propose a fusion algorithm viz. FACS which fuses the estimates of multiple participating algorithms in order to improve the sparse signal reconstruction. To alleviate the inherent drawbacks of FACS and further improve the sparse signal reconstruction, we propose another fusion algorithm called CoMACS and variants of CoMACS. For low latency applications, we propose a latency friendly fusion algorithm called pFACS. We also extend the fusion framework to the MMV problem and propose the extension of FACS called MMV-FACS. We theoretically analyse the proposed fusion algorithms and derive guarantees for performance improvement. We also show that the proposed fusion algorithms are robust against both signal and measurement perturbations. Further, we demonstrate the efficacy of the proposed algorithms via numerical experiments: (i) using sparse signals with different statistical distributions in noise-free and noisy scenarios, and (ii) using real-world ECG signals. The extensive numerical experiments show that, for a judicious choice of the participating algorithms, the proposed fusion algorithms result in a sparse signal estimate which is often better than the sparse signal estimate of the best participating algorithm. The proposed fusion framework requires toemploy multiple sparse reconstruction algorithms for sparse signal reconstruction. We also propose an iterative framework and algorithm called {IFSRA to improve the performance of a given arbitrary sparse reconstruction algorithm. We theoretically analyse IFSRA and derive convergence guarantees under signal and measurement perturbations. Numerical experiments on synthetic and real-world data confirm the efficacy of IFSRA. The proposed fusion algorithms and IFSRA are general in nature and does not require any modification in the participating algorithm(s).

Wireless sensor networks are formed by mobile devices that collect and process data from an enviroment, and transmit them to a data center wich is responsible for taking decisions. This work aims to analyze the signal reconstruction in these networks using geostatistic techniques. Three processes of kriging are used: simple, ordinary and bayesian. Three approaches to simple krigingwere found in the literature, according to the way themean of the data is estimated,were assessed themall. A newBayesian approach is proposed: use general least square to estimate the mean, and set it as a constant into the Bayesian inference. The effect of clustering techniques is assessed, namely without clusters and with clusters formed by LEACH and SKATER algorithms. Bayesian kriging presents the best qualitative results in almost all scenarios, but it is not available to systems that require fast aswers; in this case we recommend ordinary kriging. The proposed variant of Bayesian kriging reduces the time required, without hampering the quality of the reconstructed signal, but the time reduction is not enough for real-time systems / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / As Redes de Sensores sem Fios (RSsF) são conjuntos de dispositivos que obtêmamostras de fenômenos ambientais, sejam eles naturais (como, por exemplo, temperatura, pressão atmosférica, intensidade de iluminação, concentração de substâncias em cursos d água) ou antrópicos (qualidade do ar em sinais de trânsito, pressão ao longo de um oleoduto). Esses dispositivos têm despertadomuito interesse, tanto pelas suas potenciais aplicações quanto pelos desafios teóricos e tecnológicos que seu uso otimizado oferece. O objetivo deste trabalho trata da análise da reconstrução de sinais nessas redes, com base em técnicas de geoestatística. Analisam-se três processos de kriging: simples, ordinário e bayesiano. Ao simples, analisam-se três abordagens encontradas na literatura para estimação ou informação do parâmetro damédia e ao bayesiano propõe-se uma variante capaz de reduzir o tempo de processamento necessário, estimando a média por mínimos quadrados generalizados, sendo uma constante na inferência bayesiana. Leva-se em consideração o processo de agrupamento dos nós sensores, com simulações sem agrupamento e com os sensores agrupados pelos algoritmos LEACH e SKATER. O algoritmo de kriging bayesiano apresenta osmelhores resultados qualitativos namaioria dos casos,mas se torna inviável para sistemas que necessitemde respostas rápidas. Nesses casos, recomenda-se o algoritmo de kriging ordinário. A variante proposta para o kriging bayesiano reduz o tempo de computação, mas não o suficiente para sistemas de tempo real i

Les travaux de recherche de cette thèse de doctorat s’inscrivent dans le cadre de la conception d’unconvertisseur analogique-numérique (ADC, Analog-to-Digital Converter) large bande et à haute résolution afinde numériser plusieurs standards de communications sans fil. Il répond ainsi au concept de la radio logiciellerestreinte (SDR, Software Defined Radio). L’objectif visé est la reconfigurabilité par logiciel et l’intégrabilité envue d’un système radio multistandard. Les ADCs à sur-échantillonnage de type sigma-delta () s’avèrent debons candidats dans ce contexte de réception SDR multistandard en raison de leur précision accrue. Bien queleur bande passante soit réduite, il est possible de les utiliser dans une architecture en parallèle permettantd’élargir la bande passante. Nous nous proposons alors dans cette thèse de dimensionner et d’implanter unADC parallèle à décomposition fréquentielle (FBD) basé sur des modulateurs  à temps-discret pour unrécepteur SDR supportant les standards E-GSM, UMTS et IEEE802.11a. La nouveauté dans l’architectureproposée est qu’il est programmable, la numérisation d’un signal issu d’un standard donné se réalise enactivant seulement les branches concernées de l’architecture parallèle avec des sous-bandes defonctionnement et une fréquence d’échantillonnage spécifiée. De plus, le partage fréquentiel des sous-bandesest non uniforme. Après validation du dimensionnement théorique par simulation, l’étage en bande de base aété dimensionné. Cette étude conduit à la définition d’un filtre anti-repliement passif unique d’ordre 6 et detype Butterworth, permettant l’élimination du circuit de contrôle de gain automatique (AGC). L’architectureFBD requière un traitement numérique permettant de combiner les signaux à la sortie des branches enparallèle pour reconstruire le signal de sortie finale. Un dimensionnement optimisé de cet étage numérique àbase de démodulation a été proposé. La synthèse de l’étage en bande de base a montré des problèmes destabilité des modulateurs . Pour y remédier, une solution basée sur la modification de la fonction detransfert du signal (STF) afin de filtrer les signaux hors bande d’intérêt par branche a été élaborée. Unediscontinuité de phase a été également constatée dans le signal de sortie reconstruit. Une solution deraccordement de phase a été proposée. L’étude analytique et la conception niveau système ont étécomplétées par une implantation de la reconstruction numérique de l’ADC parallèle. Deux flots de conceptionont été considérés, un associé au FPGA et l’autre indépendant de la cible choisie (VHDL standard).L’architecture proposée a été validée sur un FPGA Xilinx de type VIRTEX6. Une dynamique de 74 dB a étémesurée pour le cas d’étude UMTS, ce qui est compatible avec celle requise du standard UMTS. / The work presented in this Ph.D. dissertation deals with the design of a wideband and accurate Analog-to-Digital Converter (ADC) able to digitize signals of different wireless communications standards. Thereby, itresponds to the Software Defined Radio concept (SDR). The purpose is reconfigurability by software andintegrability of the multistandard radio terminal. Oversampling  (Sigma Delta) ADCs have been interestingcandidates in this context of multistandard SDR reception thanks to their high accuracy. Although they presentlimited operating bandwidth, it is possible to use them in a parallel architecture thus the bandwidth isextended. Therefore, we propose in this work the design and implementation of a parallel frequency banddecomposition ADC based on Discrete-time  modulators in an SDR receiver handling E-GSM, UMTS andIEEE802.11a standard signals. The novelty of this proposed architecture is its programmability. Where,according to the selected standard digitization is made by activating only required branches are activated withspecified sub-bandwidths and sampling frequency. In addition the frequency division plan is non-uniform.After validation of the theoretical design by simulation, the overall baseband stage has been designed. Resultsof this study have led to a single passive 6th order Butterworth anti-aliasing filter (AAF) permitting theelimination of the automatic gain control circuit (AGC) which is an analog component. FBD architecturerequires digital processing able to recombine parallel branches outputs signals in order to reconstruct the finaloutput signal. An optimized design of this digital reconstruction signal stage has been proposed. Synthesis ofthe baseband stage has revealed  modulators stability problems. To deal with this problem, a solution basedon non-unitary STF has been elaborated. Indeed, phase mismatches have been shown in the recombinedoutput signal and they have been corrected in the digital stage. Analytic study and system level design havebeen completed by an implementation of the parallel ADC digital reconstruction stage. Two design flows havebeen considered, one associated to the FPGA and another independent of the chosen target (standard VHDL).Proposed architecture has been validated using a VIRTEX6 FPGA Xilinx target. A dynamic range over 74 dB hasbeen measured for UMTS use case, which responds to the dynamic range required by this standard.

Description of construction of analog-to-digital and digital-to-analog convertors for audio signal and distribution via wireless channel, are the objectives of my master's thesis. There are descriptions of DPS construction, design of panels and measurement of system parameters in the project, above all sampling and reconstruction of audio signal, power consumption and signal range of wireless modules. At the end is discussed real usage and suggestions for further developement.

Neurone sind anregbare Zellen, die mit Hilfe von elektrischen Signalen miteinander kommunizieren. Im allgemeinen werden eingehende Signale von den Nervenzellen in einer nichtlinearen Art und Weise verarbeitet. Wie diese Verarbeitung in einer umfassenden und exakten Art und Weise mathematisch beschrieben werden kann, ist bis heute nicht geklärt und ist Gegenstand aktueller Forschung. In dieser Arbeit untersuchen wir die nichtlineare Übertragung und Verarbeitung von Signalen durch stochastische Nervenzellen und wenden dabei zwei unterschiedliche Herangehensweisen an. Im ersten Teil der Arbeit befassen wir uns mit der Frage, auf welche Art und Weise ein Signal mit einer bekannten Zeitabhängigkeit die Rate der neuronalen Aktivität beeinflusst. Im zweiten Teil der Arbeit widmen wir uns der Rekonstruktion eingehender Signale aus der durch sie hervorgerufenen neuronalen Aktivität und beschäftigen uns mit der Abschätzung der übertragenen Informationsmenge. Die Ergebnisse dieser Arbeit demonstrieren, wie die etablierten linearen Theorien, die die Modellierung der neuronalen Aktivitätsrate bzw. die Rekonstruktion von Signalen beschreiben, um Beiträge höherer Ordnung erweitert werden können. Einen wichtigen Beitrag dieser Arbeit stellt allerdings auch die Darstellung der Signifikanz der nichtlinearen Theorien dar. Die nichtlinearen Beiträge erweisen sich nicht nur als schwache Korrekturen zu den etablierten linearen Theorien, sondern beschreiben neuartige Effekte, die durch die linearen Theorien nicht erfasst werden können. Zu diesen Effekten gehört zum Beispiel die Anregung von harmonischen Oszillationen der neuronalen Aktivitätsrate und die Kodierung von Signalen in der signalabhängigen Varianz einer Antwortvariablen. / Neurons are excitable cells which communicate with each other via electrical signals. In general, these signals are processed by the Neurons in a nonlinear fashion, the exact mathematical description of which is still an open problem in neuroscience. In this thesis, the broad topic of nonlinear signal processing is approached from two directions. The first part of the thesis is devoted to the question how input signals modulate the neural response. The second part of the thesis is concerned with the nonlinear reconstruction of input signals from the neural output and with the estimation of the amount of the transmitted information. The results of this thesis demonstrate how existing linear theories can be extended to capture nonlinear contributions of the signal to the neural response or to incorporate nonlinear correlations into the estimation of the transmitted information. More importantly, however, our analysis demonstrates that these extensions do not merely provide small corrections to the existing linear theories but can account for qualitatively novel effects which are completely missed by the linear theories. These effects include, for example, the excitation of harmonic oscillations in the neural firing rate or the estimation of information for systems with a signal-dependent output variance.

Bar code stores information in the form of series of bars and gaps with various widths, and therefore can be considered as an example of bilevel (square) signal. Magnetic bar codes are created by applying slightly ferromagnetic material to a substrate. Sensing is done by reading oscillator, whose frequency is modulated by presence of the mentioned ferromagnetic material. Signal from the oscillator is then subjected to frequency demodulation. Due to temperature drift of the reading oscillator, the demodulated signal is accompanied by DC drift. Method for removal of the drift is introduced. Also, drift-insensitive detection of presence of a bar code is described. Reading bar codes is complicated by convolutional distortion, which is result of spatially dispersed sensitivity of the sensor. Effect of the convolutional distortion is analogous to low-pass filtering, causing edges to be smoothed and overlapped, and making their detection difficult. Characteristics of convolutional distortion can be summarized into point-spread function (PSF). In case of magnetic bar codes, the shape of the PSF can be known in advance, but not its width of DC transfer. Methods for estimation of these parameters are discussed. The signal needs to be reconstructed (into original bilevel form) before decoding can take place. Variational methods provide effective way. Their core idea is to reformulate reconstruction as an optimization problem of functional minimization. The functional can be extended by other functionals (regularizations) in order to considerably improve results of reconstruction. Principle of variational methods will be shown, including examples of use of various regularizations. All algorithm and methods (including frequency demodulation of signal from reading oscillator) are digital. They are implemented as a program for a microcontroller from the PIC32 family, which offers high computing power, so that even blind deconvolution (when the real PSF also needs to be found) can be finished in a few seconds. The microcontroller is part of magnetic bar code reader, whose hardware allows the read information to be transferred to personal computer via the PS/2 interface or USB (by emulating key presses on virtual keyboard), or shown on display.