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

In this paper, we turn the interpolation problem of coarsely-sampled data into a denoising problem. From this point of view, we illustrate the benefit of random sampling at sub-Nyquist rate over regular sampling at the same rate. We show that, using nonlinear sparsity promoting optimization, coarse random sampling may actually lead to significantly better wavefield reconstruction than equivalent regularly sampled data.

No description available.

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

Vena contracta width (VCW) and effective regurgitant orifice area (EROA) are well established methods for evaluating mitral regurgitation using transesophageal echocardiography (TEE). For color-flow Doppler (CF) measurements Nyquist limit of 50–60 cm/s is recommended. Aim of the study was to investigate the effectiveness of a baseline shift of the Nyquist limit for these measurements. After a comprehensive 2-dimensional (2D) TEE examination, the mitral regurgitation jet was acquired with a Nyquist limit of 50 cm/s (NL50) along with a baseline shift to 37.5 cm/s (NL37.5) using CF. Moreover a real time 3-dimensional (RT 3D) color complete volume dataset was stored with a Nyquist limit of 50 cm/s (NL50) and 37.5 cm/s (NL37.5). Vena contracta width (VCW) as well as Proximal Isovelocity Surface Area (PISA) derived EROA were measured based on 2D TEE and compared to RT 3D echo measurements for vena contracta area (VCA) using planimetry method. Correlation between VCA 3D NL50 and VCW NL50 was 0.29 (p<0.05) compared to 0.6 (p<0.05) using NL37.5. Correlation between VCA 3D NL50 and EROA 2D NL50 was 0.46 (p<0.05) vs. 0.6 (p<0.05) EROA 2D NL37.5. Correlation between VCA 3D NL37.5 and VCW NL50 was 0.45 (p<0.05) compared to 0.65 (p<0.05) using VCW NL37.5. Correlation between VCA 3D NL37.5 and EROA 2D NL50 was 0.41 (p<0.05) vs. 0.53 (p<0.05) using EROA 2D NL37.5. Baseline shift of the NL to 37.5 cm/s improves the correlation for VCW and EROA when compared to RT 3D NL50 planimetry of the vena contracta area. Baseline shift in RT 3D to a NL of 37.5 cm/s shows similar results like NL50.

Nous proposons un nouveau schéma d’échantillonnage non uniforme périodique appelé Système d’Échantillonnage Non Uniforme en Radio Intelligente (SENURI). Notre schéma détecte la localisation spectrale des bandes actives dans la bande totale échantillonnée afin de réduire la fréquence moyenne d’échantillonnage, le nombre d’échantillons prélevé et par conséquent la consommation d’énergie au niveau du traitement numérique. La fréquence moyenne d’échantillonnage du SENURI dépend uniquement du nombre de bandes contenues dans le signal d’entrée x(t). Il est nettement plus performant, en termes d’erreur quadratique, qu’une architecture classique d’échantillonnage non uniforme périodique constituée de p branches, lorsque le spectre de x(t) change dynamiquement. / In this work we consider the problem of designing an effective sampling scheme for sparse multi-band signals. Based on previous results on periodic non-uniform sampling (Multi-Coset) and using the well known Non-Uniform Fourier Transform through Bartlett’s method for Power Spectral Density estimation, we propose a new sampling scheme named the Dynamic Single Branch Non-uniform Sampler (DSB-NUS). The idea of the proposed scheme is to reduce the average sampling frequency, the number of samples collected, and consequently the power consumption of the Analog to Digital Converter (ADC). In addition to that our proposed method detects the location of the bands in order to adapt the sampling rate. In this thesis, we show through simulation results that compared to existing multi-coset based samplers, our proposed sampler provides superior performance, both in terms of sampling rate and energy consumption. It is notconstrained by the inflexibility of hardware circuitry and is easily reconfigurable. We also show the effect of the false detection of active bands on the average sampling rate of our new adaptive non-uniform sub-Nyquist sampler scheme.

A Eletrodinâmica Estocástica é uma combinação da Eletrodinâmica Clássica e a hipótese adicional de que existem campos eletromagnéticos aleatórios, independentes da temperatura, denominados radiação de ponto-zero ou flutuações do vácuo, responsáveis pelo surgimento de certas propriedades peculiares dos sistemas microscópicos, geralmente descritas pela Mecânica Quântica. Diversos novos resultados da teoria são apresentados nesse trabalho. No capítulo 1, é feita uma breve introdução aos principais conceitos e pressupostos da Eletrodinâmica Estocástica, necessários para melhor compreensão dos capítulos seguintes. No capítulo 2, a atuação dos campos do vácuo no indutor de um circuito elétrico simples é estudada. Conclui-se que deve existir um tipo de ruído na voltagem do circuito, adicional ao ruído de Nyquist-Johnson, que pode ser medido dependendo da magnitude de certos parâmetros do circuito e sob certas condições de temperatura. No capítulo 3, é estudado o comportamento de uma partícula eletrizada em um potencial metaestável, com uma barreira de potencial, sujeita às flutuações da radiação térmica e de ponto-zero. Mostra-se que, mesmo à temperatura muito baixa (T -> 0), as flutuações do vácuo ainda são capazes de promover o escape da partícula através da barreira de potencial. A Mecânica Quântica atribui o fenômeno ao tunelamento da partícula através da barreira. Um conjunto de dados experimentais são analisados e observa-se que a descrição da Eletrodinâmica Estocástica produz um excelente acordo com eles. No capítulo 4, é mostrado que os formalismos de Heisenberg e Schrodinger da Mecânica Quântica deixam de ser equivalentes quando se leva em conta os campos do vácuo nos cálculos. Dirac foi o primeiro a apontar essa não equivalência para casos da Eletrodinâmica Quântica Relativísitica. Um exemplo bem mais simples é apresentado, o oscilador harmônico eletrizado, em interação com o campo eletromagnético do vácuo. / The Stochastic Electrodynamics Theory is a combination of Classical Electrodynamics and the additional hypothesis that temperature-independent stochastic electromagnetic fields do exist. These electromagnetic fields are called zero-point radiation or vacuum fluctuations and are responsible for some peculiar properties of macroscopic systems, usually described by Quantum Mechanics. Some new results of the theory are given in this work. In chapter 1, a brief introduction of the main concepts and hypothesis of the Stochastic Electrodynamics Theory are given. They are necessary for a better understanding of the following chapters. In chapter 2, the influence of vacuum fields at the inductor of a simple electric circuit is studied. One concludes that a certain type of noise in the voltage, which is additional to the NyquistJohnson noise, must exist and can be measured depending on certain circuit parameters and under certain temperatures. In chapter 3, one studies the behavior of an electrified particle inside a metastable potential with a potential barrier, under the influence of the fluctuations of thermal and zero-point radiations. It is shown that, even if the temperature is very low (T -> 0), the vacuum fluctuations are still responsible for the escape of the particle through the potential barrier. Quantum Mechanics relates this phenomenon to the tunneling of the particle through the potential barrier. Experimental data are analyzed and it is shown that the description of Stochastic Electrodynamics gives an excellent agreement with them. In chapter 4, it is shown that the Schrodinger and Heisenberg pictures of Quantum Mechanics are not equivalent when the vacuum fields are taken into account. Dirac was the first to point out this non-equivalence for Relativistic Quantum Electrodynamics. A simpler example of this non-equivalence is shown in the context of Stochastic Electrodynamics: an electrified harmonic oscillator interacting with the electromagnetic vacuum fields.

A Eletrodinâmica Estocástica é uma combinação da Eletrodinâmica Clássica e a hipótese adicional de que existem campos eletromagnéticos aleatórios, independentes da temperatura, denominados radiação de ponto-zero ou flutuações do vácuo, responsáveis pelo surgimento de certas propriedades peculiares dos sistemas microscópicos, geralmente descritas pela Mecânica Quântica. Diversos novos resultados da teoria são apresentados nesse trabalho. No capítulo 1, é feita uma breve introdução aos principais conceitos e pressupostos da Eletrodinâmica Estocástica, necessários para melhor compreensão dos capítulos seguintes. No capítulo 2, a atuação dos campos do vácuo no indutor de um circuito elétrico simples é estudada. Conclui-se que deve existir um tipo de ruído na voltagem do circuito, adicional ao ruído de Nyquist-Johnson, que pode ser medido dependendo da magnitude de certos parâmetros do circuito e sob certas condições de temperatura. No capítulo 3, é estudado o comportamento de uma partícula eletrizada em um potencial metaestável, com uma barreira de potencial, sujeita às flutuações da radiação térmica e de ponto-zero. Mostra-se que, mesmo à temperatura muito baixa (T -> 0), as flutuações do vácuo ainda são capazes de promover o escape da partícula através da barreira de potencial. A Mecânica Quântica atribui o fenômeno ao tunelamento da partícula através da barreira. Um conjunto de dados experimentais são analisados e observa-se que a descrição da Eletrodinâmica Estocástica produz um excelente acordo com eles. No capítulo 4, é mostrado que os formalismos de Heisenberg e Schrodinger da Mecânica Quântica deixam de ser equivalentes quando se leva em conta os campos do vácuo nos cálculos. Dirac foi o primeiro a apontar essa não equivalência para casos da Eletrodinâmica Quântica Relativísitica. Um exemplo bem mais simples é apresentado, o oscilador harmônico eletrizado, em interação com o campo eletromagnético do vácuo. / The Stochastic Electrodynamics Theory is a combination of Classical Electrodynamics and the additional hypothesis that temperature-independent stochastic electromagnetic fields do exist. These electromagnetic fields are called zero-point radiation or vacuum fluctuations and are responsible for some peculiar properties of macroscopic systems, usually described by Quantum Mechanics. Some new results of the theory are given in this work. In chapter 1, a brief introduction of the main concepts and hypothesis of the Stochastic Electrodynamics Theory are given. They are necessary for a better understanding of the following chapters. In chapter 2, the influence of vacuum fields at the inductor of a simple electric circuit is studied. One concludes that a certain type of noise in the voltage, which is additional to the NyquistJohnson noise, must exist and can be measured depending on certain circuit parameters and under certain temperatures. In chapter 3, one studies the behavior of an electrified particle inside a metastable potential with a potential barrier, under the influence of the fluctuations of thermal and zero-point radiations. It is shown that, even if the temperature is very low (T -> 0), the vacuum fluctuations are still responsible for the escape of the particle through the potential barrier. Quantum Mechanics relates this phenomenon to the tunneling of the particle through the potential barrier. Experimental data are analyzed and it is shown that the description of Stochastic Electrodynamics gives an excellent agreement with them. In chapter 4, it is shown that the Schrodinger and Heisenberg pictures of Quantum Mechanics are not equivalent when the vacuum fields are taken into account. Dirac was the first to point out this non-equivalence for Relativistic Quantum Electrodynamics. A simpler example of this non-equivalence is shown in the context of Stochastic Electrodynamics: an electrified harmonic oscillator interacting with the electromagnetic vacuum fields.

Avec la multiplication des terminaux mobiles et le foisonnement des objets dits « connectés », on assiste à la montée d'un besoin de moyens de communication à tout endroit et en toute situation, accompagné d'un encombrement spectral toujours plus important. Dans ce contexte, si la capacité d'adaptation au canal des modulations multiporteuses permet de bien s'accommoder du besoin de communication en tout endroit, les techniques actuelles, en particulier l'OFDM, souffrent d'une mauvaise localisation fréquentielle et d'un mauvais facteur de crête, ce qui limite leur utilisation dans un contexte embarqué et/ou en présence de fortes contraintes spectrales. Dans cette thèse, nous étudions les modulations multiporteuses au-delà de la cadence de Nyquist. En augmentant la densité de signalisation, ces dernières permettent d'augmenter l'efficacité spectrale. Cela est cependant contrebalancé par l'apparition d'auto-interférence, ce qui rend la réception plus délicate.Sur canal à bruit additif blanc gaussien, on montre comment choisir des impulsions de mise en forme maximisant le rapport signal à interférence plus bruit. On montre que ces dernières permettent d'obtenir une turbo-égalisation linéaire de l'auto-interférence minimisant l'erreur quadratique moyenne. Nos travaux mettent en évidence que ces mêmes impulsions permettent également de réduire le facteur de crête à mesure que la densité augmente. Enfin, sur canal sélectif en fréquence, on vérifie que l'approximation du canal par un coefficient par sous-porteuse est toujours possible. Ces résultats montrent que ce nouveau type de modulation permet d'augmenter l'efficacité spectrale tout en conservant la capacité d'adaptation au canal intrinsèque aux modulations multiporteuses. / With an increasing number of mobile terminals coupled with a large spreading of so-called "smart devices", we can see a growing demand for effective communication means in any place and in any situation.This goes with a more and more overcrowded spectrum.In this context, multicarrier modulations are good candidates to allow effective communication in any place.However current techniques, OFDM in particular, suffer from a bad time--frequency localization and peak-to-average power ratio, limiting their relevancy in an embedded context, or in scenarios with severe spectral constraints.In this thesis, we study faster-than-Nyquist multicarrier modulations.This kind of modulation allow for an increase in spectral efficiency by means of an increase in signaling density.This, in compensation, comes at the price of unavoidable self-interference, which makes demodulation harder.On an additive white Gaussian noise channel, we show how to carefully chose pulse-shapes that maximize signal-to-interference-plus-noise ratio.We show that these particular pulse-shapes yields a linear turbo-equalization of self-interference minimizing the mean squared error.Next, our work highlights the capability of these optimal pulse-shapes to reduce peak-to-average power ratio as density rises.Lastly, on frequency selective channels, we confirm that low complexity equalization using one tap by subcarrier is still possible.These results show how this new modulation technique helps increasing spectral efficiency while keeping what made multicarrier modulations popular: good adaptation to transmission channels.

Nous proposons un nouveau schéma d’échantillonnage non uniforme périodique appelé Système d’Échantillonnage Non Uniforme en Radio Intelligente (SENURI). Notre schéma détecte la localisation spectrale des bandes actives dans la bande totale échantillonnée afin de réduire la fréquence moyenne d’échantillonnage, le nombre d’échantillons prélevé et par conséquent la consommation d’énergie au niveau du traitement numérique. La fréquence moyenne d’échantillonnage du SENURI dépend uniquement du nombre de bandes contenues dans le signal d’entrée x(t). Il est nettement plus performant, en termes d’erreur quadratique, qu’une architecture classique d’échantillonnage non uniforme périodique constituée de p branches, lorsque le spectre de x(t) change dynamiquement. / In this work we consider the problem of designing an effective sampling scheme for sparse multi-band signals. Based on previous results on periodic non-uniform sampling (Multi-Coset) and using the well known Non-Uniform Fourier Transform through Bartlett’s method for Power Spectral Density estimation, we propose a new sampling scheme named the Dynamic Single Branch Non-uniform Sampler (DSB-NUS). The idea of the proposed scheme is to reduce the average sampling frequency, the number of samples collected, and consequently the power consumption of the Analog to Digital Converter (ADC). In addition to that our proposed method detects the location of the bands in order to adapt the sampling rate. In this thesis, we show through simulation results that compared to existing multi-coset based samplers, our proposed sampler provides superior performance, both in terms of sampling rate and energy consumption. It is notconstrained by the inflexibility of hardware circuitry and is easily reconfigurable. We also show the effect of the false detection of active bands on the average sampling rate of our new adaptive non-uniform sub-Nyquist sampler scheme.