Output Filter Aware Optimization of the Noise Shaping Properties of {\Delta}{\Sigma} Modulators via Semi-Definite Programming

The Noise Transfer Function (NTF) of {\Delta}{\Sigma} modulators is typically designed after the features of the input signal. We suggest that in many applications, and notably those involving D/D and D/A conversion or actuation, the NTF should instead be shaped after the properties of the output/reconstruction filter. To this aim, we propose a framework for optimal design based on the Kalman-Yakubovich-Popov (KYP) lemma and semi-definite programming. Some examples illustrate how in practical cases the proposed strategy can outperform more standard approaches.Comment: 14 pages, 18 figures, journal. Code accompanying the paper is available at http://pydsm.googlecode.co

Adaptive smoothness constraint image multilevel fuzzy enhancement algorithm

For the problems of poor enhancement effect and long time consuming of the traditional algorithm, an adaptive smoothness constraint image multilevel fuzzy enhancement algorithm based on secondary color-to-grayscale conversion is proposed. By using fuzzy set theory and generalized fuzzy set theory, a new linear generalized fuzzy operator transformation is carried out to obtain a new linear generalized fuzzy operator. By using linear generalized membership transformation and inverse transformation, secondary color-to-grayscale conversion of adaptive smoothness constraint image is performed. Combined with generalized fuzzy operator, the region contrast fuzzy enhancement of adaptive smoothness constraint image is realized, and image multilevel fuzzy enhancement is realized. Experimental results show that the fuzzy degree of the image is reduced by the improved algorithm, and the clarity of the adaptive smoothness constraint image is improved effectively. The time consuming is short, and it has some advantages

Study of phase noise in optical coherent systems

Le bruit de phase est un problème important dans la conception de systèmes cohérents optiques. Bien que le bruit de phase soit étudié énormément dans les communications sans fil, certains aspects de bruit de phase sont nouveaux dans des systèmes cohérents optiques. Dans cette thèse, nous explorons les statistiques de bruit de phase dans les systèmes optiques cohérentes et proposons une nouvelle technique pour améliorer la robustesse du système envers le bruit de phase. Notre première contribution traite de l’étude des statistiques de bruit de phase en présence de compensation électronique de la dispersion chromatique (CD) dans des systèmes cohérents. Nous montrons que le modèle proposé précédemment pour l’interaction de CD avec bruit de phase doit être modifié à cause d’un modèle trop simple pour la récupération de phase. Nous dérivons une expression plus précise pour le bruit de phase estimé par la récupération de phase avec décision dirigée (DD), et utilisons cette expression pour modifier les statistiques de décision pour les symboles reçus. Nous calculons le taux d’erreur binaire (BER) pour le format de transmission DQPSK semi-analytiquement en utilisant nos statistiques de décision modifiées et montrons que pour la récupération de phase idéale, le BER semi-analytique est bien assorti avec le BER simulé avec la technique Monte-Carlo (MC). Notre deuxième contribution est l’adaptation d’une technique de codage MLCM pour les systèmes cohérents limités par le bruit de phase et le bruit blanc additif Gaussien (AWGN). Nous montrons que la combinaison d’une constellation optimisée pour le bruit de phase avec MLCM offre un système robuste à complexité modérée. Nous vérifions que la performance de MLCM dans des systèmes cohérents avec constellations 16-aires se détériorés par le bruit de phase non-linéaire et de Wiener. Pour le bruit de phase non-linéaire, notre conception de MLCM démontre une performance supérieure par rapport àune conception de MLCM déjà présente dans la littérature. Pour le bruit de phase de Wiener, nous comparons deux format de transmission, constellations carrées et optimisée pour bruit de phase, et deux techniques de codage, MLCM et codage à débit uniforme. Nos résultats expérimentaux pour BER après codage suivent les mêmes tendances que le BER simulé et confirment notre conception.Phase noise is an important issue in designing today’s optical coherent systems. Although phase noise is studied heavily in wireless communications, some aspects of phase noise are novel in optical coherent systems. In this thesis we explore phase noise statistics in optical coherent systems and propose a novel technique to increase system robustness toward phase noise. Our first contribution deals with the study of phase noise statistics in the presence of electronic chromatic dispersion (CD) compensation in coherent systems. We show that previously proposed model for phase noise and CD interaction must be modified due to an overly simple model of carrier phase recovery. We derive a more accurate expression for the estimated phase noise of decision directed (DD) carrier phase recovery, and use this expression to modify the decision statistics of received symbols. We calculate bit error rate (BER) of a differential quadrature phase shift keying (DQPSK) system semi-analytically using our modified decision statistics and show that for ideal DD carrier phase recovery the semi-analytical BER matches the BER simulated via Monte-Carlo (MC) technique. We show that the semi-analytical BER is a lower bound of simulated BER from Viterbi-Viterbi (VV) carrier phase recovery for a wide range of practical system parameters. Our second contribution is concerned with adapting a multi-level coded modulation (MLCM) technique for phase noise and additive white Gaussian noise (AWGN) limited coherent system. We show that the combination of a phase noise optimized constellation with MLCM offers a phase-noise robust system at moderate complexity. We propose a numerical method to design set-partitioning (mapping bits to symbols) and optimizing code rates for minimum block error rate (BLER).We verify MLCM performance in coherent systems of 16-ary constellations impaired by nonlinear and Wiener phase noise. For nonlinear phase noise, superior performance of our MLCM design over a previously designed MLCM system is demonstrated in terms of BLER. For Wiener phase noise, we compare optimized and square 16-QAM constellations assuming either MLCM or uniform rate coding. We compare post forward error correction (FEC) BER in addition to BLER by both simulation and experiment and show that superior BLER performance is translated into post FEC BER. Our experimental post FEC BER results follow the same trends as simulated BER, validating our design

A combined first and second order variational approach for image reconstruction

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure

Wave-based sensor, actuator and optimizer

Programa doutoral em Sistemas Avançados de Engenharia para a Indústria (AESI)A presente tese explora a utilização de ondas para abordar dois desafios significativos na indústria automóvel. O primeiro desafio consiste no desenvolvimento de um sistema de cancelamento ativo de ruído (ANC) que possa reduzir os ruídos não estacionários no compartimento de passageiros de um veículo. O segundo desafio é criar uma metodologia de conceção ótima para sensores de posição indutivos capazes de medir deslocamentos lineares, rotacionais e angulares. Para abordar o primeiro desafio, foi desenvolvido de um sistema ANC onde wavelets foram combinadas com um banco de filtros adaptativos. O sistema foi implementado em uma FPGA, e testes demonstraram que o sistema pode reduzir o ruído não estacionário em um ambiente acústico aberto e não controlado em 9 dB. O segundo desafio foi abordado através de uma metodologia que combina um algoritmo genético com um método numérico rápido para otimizar um sensor de posição indutivo. O método numérico foi usado para simular o campo eletromagnético associado à geometria do sensor, permitindo a maximização da corrente induzida nas bobinas recetoras e a minimização da não-linearidade no sensor. A minimização da não-linearidade foi conseguida através do desenho (layout) das bobinas que compõem o sensor. Sendo este otimizado no espaço de Fourier através da adição de harmónicos apropriados na geometria. As melhores geometrias otimizadas apresentaram uma não-linearidade inferior a 0,01% e a 0,25% da escala total para os sensores de posição angular e linear, respetivamente, sem calibração por software. O sistema ANC proposto tem o potencial de melhorar o conforto dos ocupantes do veículo, reduzindo o ruído indesejado dentro do compartimento de passageiros. Isso poderia reduzir o uso de materiais de isolamento acústico no veículo, levando a um veículo mais leve e, em última análise, a uma redução no consumo de energia. A metodologia desenvolvida para sensores de posição indutivos contribui para o estado da arte de sensores de posição eficientes e económicos, o que é crucial para os requisitos complexos da indústria automóvel. Essas contribuições têm implicações para o desenho de sistemas automotivos, com requisitos de desempenho e considerações ambientais e económicas.This thesis explores the use of waves to tackle two major engineering challenges in the automotive industry. The first challenge is the development of an Active Noise Cancelling (ANC) system that can effectively reduce non-stationary noise inside a vehicle’s passenger compartment. The second challenge is the optimization of an inductive position sensor design methodology capable of measuring linear, rotational, and angular displacements. To address the first challenge, this work designs an ANC system that employs wavelets combined with a bank of adaptive filters. The system was implemented in an FPGA, and field tests demonstrate its ability to reduce non-stationary noise in an open and uncontrolled acoustic environment by 9 dB. The second challenge was tackled by proposing a new approach that combines a genetic algorithm with a fast and lightweight numerical method to optimize the geometry of an inductive position sensor. The numerical method is used to simulate the sensor’s electromagnetic field, allowing for the maximization of induced current on the receiver coils while minimizing the sensor’s non-linearity. The non-linearity minimization was achieved through its unique sensor’s coils design optimized in the Fourier space by adding the appropriate harmonics to the coils’ geometry. The best optimized geometries exhibited a non-linearity of less than 0.01% and 0.25% of the full scale for the angular and linear position sensors, respectively. Both results were achieved without the need for signal calibration or post-processing manipulation. The proposed ANC system has the potential to enhance the comfort of vehicle occupants by reducing unwanted noise inside the passenger compartment. Moreover, it has the potential to reduce the use of acoustic insulation materials in the vehicle, leading to a lighter vehicle and ultimately reducing energy consumption. The developed methodology for inductive position sensors represents a state-of-the-art contribution to efficient and cost-effective position sensor design, which is crucial for meeting the complex requirements of the automotive industry.I would like to thank the Fundação para a Ciência e Tecnologia (FCT) and Bosch Car Multimedia for funding my PhD (grant PD/BDE/142901/2018)