Spectrum sensing is the process of identifying the frequencies of a spectrum in which Signals Of Interest (SOI) are present. In case of continuous time signals present in a wideband spectrum, the information rate is seen to be much less than that suggested by its bandwidth and are therefore known as sparse signals. A review of the literature in [1] and [2] indicates that two of the many techniques used in wideband spectrum sensing of sparse signals are the Wideband Compressive Radio Receiver (WCRR) for multitoned signals and the mixed analog digital system for multiband signals. In both of these techniques even though the signals are sampled at sub-Nyquist rates using Compressive Sampling (CS), the recovery algorithms used by them are different from that of CS. In WCRR, a simple correlation function is used for the detection of carrier frequencies and in a mixed analog digital system, a simple digital algorithm is used for the identification of frequency support. Through a literature survey, we could identify that a VHSIC hardware descriptive ModelSim simulation model for wideband spectrum sensing of multitoned and multiband signals using sub Nyquist sampling does not exist. If a ModelSim simulation model can be developed using VHDL codes, it can be easily adapted for FPGA implementation leading to the development of a realistic hardware prototype for use in Cognitive Radio (CR) communication systems. The research work reported through this dissertation deals with the implementation of simulation models of WCRR and mixed analog digital system in ModelSim by making use of VHDL coding. Algorithms corresponding to different blocks contained in the conceptual design of these models have been formulated prior to the coding phase. After the coding phase, analyses of the models are performed using test parameter choices to ensure that they meet the design requirements. Different parametric choices are then assigned for the parametric study and a sufficient number of iterations of these simulations were carried out to verify and validate these models. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2014

Spectrum sensing is the process of identifying the frequencies of a spectrum in which Signals Of Interest (SOI) are present. In case of continuous time signals present in a wideband spectrum, the information rate is seen to be much less than that suggested by its bandwidth and are therefore known as sparse signals. A review of the literature in [1] and [2] indicates that two of the many techniques used in wideband spectrum sensing of sparse signals are the Wideband Compressive Radio Receiver (WCRR) for multitoned signals and the mixed analog digital system for multiband signals. In both of these techniques even though the signals are sampled at sub-Nyquist rates using Compressive Sampling (CS), the recovery algorithms used by them are different from that of CS. In WCRR, a simple correlation function is used for the detection of carrier frequencies and in a mixed analog digital system, a simple digital algorithm is used for the identification of frequency support. Through a literature survey, we could identify that a VHSIC hardware descriptive ModelSim simulation model for wideband spectrum sensing of multitoned and multiband signals using sub Nyquist sampling does not exist. If a ModelSim simulation model can be developed using VHDL codes, it can be easily adapted for FPGA implementation leading to the development of a realistic hardware prototype for use in Cognitive Radio (CR) communication systems. The research work reported through this dissertation deals with the implementation of simulation models of WCRR and mixed analog digital system in ModelSim by making use of VHDL coding. Algorithms corresponding to different blocks contained in the conceptual design of these models have been formulated prior to the coding phase. After the coding phase, analyses of the models are performed using test parameter choices to ensure that they meet the design requirements. Different parametric choices are then assigned for the parametric study and a sufficient number of iterations of these simulations were carried out to verify and validate these models. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2014

Cette thèse porte sur l'utilisation du BLASSO, un problème d'optimisation convexe en dimension infinie généralisant le LASSO aux mesures, pour la super-résolution de sources ponctuelles. Nous montrons d'abord que la stabilité du support des solutions, pour N sources se regroupant, est contrôlée par un objet appelé pré-certificat aux 2N-1 dérivées nulles. Quand ce pré-certificat est non dégénéré, dans un régime de petit bruit dont la taille est contrôlée par la distance minimale séparant les sources, le BLASSO reconstruit exactement le support de la mesure initiale. Nous proposons ensuite l'algorithme Sliding Frank-Wolfe, une variante de l'algorithme de Frank-Wolfe avec déplacement continu des amplitudes et des positions, qui résout le BLASSO. Sous de faibles hypothèses, cet algorithme converge en un nombre fini d'itérations. Nous utilisons cet algorithme pour un problème 3D de microscopie par fluorescence en comparant trois modèles construits à partir des techniques PALM/STORM. / This thesis studies the noisy sparse spikes super-resolution problem for positive measures using the BLASSO, an infinite dimensional convex optimization problem generalizing the LASSO to measures. First, we show that the support stability of the BLASSO for N clustered spikes is governed by an object called the (2N-1)-vanishing derivatives pre-certificate. When it is non-degenerate, solving the BLASSO leads to exact support recovery of the initial measure, in a low noise regime whose size is controlled by the minimal separation distance of the spikes. In a second part, we propose the Sliding Frank-Wolfe algorithm, based on the Frank-Wolfe algorithm with an added step moving continuously the amplitudes and positions of the spikes, that solves the BLASSO. We show that, under mild assumptions, it converges in a finite number of iterations. We apply this algorithm to the 3D fluorescent microscopy problem by comparing three models based on the PALM/STORM technics.