Adaptive filtering has grown to become a fundamental topic in signal processing, increasingly attracting attention from the community. Important factors in this popularization were their low computational complexity and model-free nature, adapting even to nonstationary characteristics of the systems and/or signals under study. Nevertheless, many adaptive algorithms introduce trade-offs, for instance, between convergence rate, nonstationary signals tracking, and steady-state error, which can hinder their use in practical applications. Furthermore, some adaptive filters can become unstable when word length is reduced and/or the input data are highly correlated. Recently, combination of adaptive filters was put forward as a solution for such issues. This approach consists in combining a pool of filters by means of a supervisor that attempts to make the overall system at least as good (usually in the mean-square sense) as the best filter in the set. Examples of these structures have been shown to successfully solve this problem, although well-known limitations remain to be addressed. Moreover, due to the relative novelty of this topic, developments in combination of adaptive filters are difficult to accommodate into a common theoretical framework. This work studies combination of adaptive filters and addresses the aforementioned issue by (i) classifying the existing combinations and proposing a taxonomy that exposes the similarities and differences in their forms; (ii) proposing new combinations; (iii) devising a general framework for studying combinations of adaptive filters and using such framework in performance analyses. / Filtragem adaptativa vem ganhando destaque desde seu surgimento tornando-se um tópico de estudo fundamental em processamento de sinais. A versatilidade de dispensarem total conhecimento das propriedades estatísticas dos sinais, aliada à simplicidade computacional de seus métodos, foram importantes fatores em sua consagração. Apesar disto, muitos filtros adaptativos apresentam compromissos envolvendo, por exemplo, velocidade de convergência, rastreamento de sinais não-estacionários e erro em regime, que podem dificultar sua aplicação na prática. Ademais, alguns algoritmos adaptativos são instáveis quando suas entradas são altamente correlacionados e/ou a precisão dos cálculos é reduzida. Uma solução recente para estes problemas é o uso de combinações de filtros adaptativos. Esta abordagem baseia-se em combinar um conjunto de filtros por meio de um supervisor que procura fazer com que o sistema global seja pelo menos tão bom (em geral no sentido quadrático médio) quanto o melhor filtro do conjunto. Exemplos destas estruturas já mostraram a eficácia deste método, apesar de ainda existirem reconhecida limitações. Além disso, em se tratando de um tópico relativamente recente, os desenvolvimentos na área de combinação de filtros adaptativos não possuem uma estrutura teórica unificada. Este trabalho propõe abordar estas questões (i) classificando as combinações existentes e criando uma taxonomia que explicite semelhanças e diferenças entre elas; (ii) introduzindo novas combinações; e (iii) desenvolvendo uma forma unificada de descrever combinações de filtros adaptativos e usando-a em análises de desempenho.

This document introduces a new class of adaptive filters, namely Geometric- Algebra Adaptive Filters (GAAFs). Those are generated by formulating the underlying minimization problem (a least-squares cost function) from the perspective of Geometric Algebra (GA), a comprehensive mathematical language well-suited for the description of geometric transformations. Also, differently from the usual linear algebra approach, Geometric Calculus (the extension of Geometric Algebra to differential calculus) allows to apply the same derivation techniques regardless of the type (subalgebra) of the data, i.e., real, complex-numbers, quaternions etc. Exploiting those characteristics, among others, a general leastsquares cost function is posed, from which two types of GAAFs are designed. The first one, called standard, provides a generalization of regular adaptive filters for any subalgebra of GA. From the obtained update rule, it is shown how to recover the following least-mean squares (LMS) adaptive filter variants: real-entries LMS, complex LMS, and quaternions LMS. Mean-square analysis and simulations in a system identification scenario are provided, showing almost perfect agreement for different levels of measurement noise. The second type, called pose estimation, is designed to estimate rigid transformations { rotation and translation - in n-dimensional spaces. The GA-LMS performance is assessed in a 3-dimensional registration problem, in which it is able to estimate the rigid transformation that aligns two point clouds that share common parts. / Este documento introduz uma nova classe de filtros adaptativos, entitulados Geometric-Algebra Adaptive Filters (GAAFs). Eles s~ao projetados via formulação do problema de minimização (uma função custo de mínimos quadrados) do ponto de vista de álgebra geométrica (GA), uma abrangente linguagem matemática apropriada para a descrição de transformações geométricas. Adicionalmente, diferente do que ocorre na formulação com álgebra linear, cálculo geométrico (a extensão de álgebra geométrica que possibilita o uso de cálculo diferencial) permite aplicar as mesmas técnicas de derivação independentemente do tipo de dados (subálgebra), isto é, números reais, números complexos, quaternions etc. Usando essas e outras características, uma função custo geral de mínimos quadrados é proposta, da qual dois tipos de GAAFs são gerados. O primeiro, chamado standard, generaliza filtros adaptativos da literatura concebidos sob a perspectiva de subálgebras de GA. As seguintes variantes do filtro least-mean squares (LMS) s~ao obtidas como casos particulares: LMS real, LMS complexo e LMS quaternions. Uma análise mean-square é desenvolvida e corroborada por simulações para diferentes níveis de ruído de medição em um cenário de identificação de sistemas. O segundo tipo, chamado pose estimation, é projetado para estimar transformações rígidas - rotação e translação { em espaços n-dimensionais. A performance do filtro GA-LMS é avaliada em uma aplicação de alinhamento tridimensional na qual ele estima a tranformação rígida que alinha duas nuvens de pontos com partes em comum.

Este trabalho tem a finalidade de analisar algumas técnicas de processamento do sinal mioelétrico, de forma a possibilitar uma posterior implementação de um circuito, que reconheça este sinal e apresente como saída um sinal de controle a ser utilizado em sistemas de reabilitação. Foram simuladas e avaliadas três técnicas de filtragem para o sinal mioelétrico, a fim de atenuar a interferência dos principais ruídos que corrompem este sinal. As técnicas avaliadas foram: filtragem digital clássica; cancelamento de ruído adaptativo e reconstrução do sinal por meio das componentes obtidas pela transformada wavelet. Também foi implementado e analisado um sistema simplificado de reconhecimento dos padrões para este sinal, realizado por meio de uma rede neural artificial, em que foi aplicado em sua entrada o próprio sinal mioelétrico e não suas características obtidas por processamentos matemáticos. Diante dos resultados obtidos os canceladores de ruído adaptativos apresentaram melhores resultados com relação às outras técnicas de filtragem. Apesar de não ter sido adequada para a filtragem, a transformada wavelet mostrou-se uma poderosa ferramenta de análise de sinais, em virtude da sua característica multiresolução. A técnica utilizada para reconhecer os padrões do sinal mostrou bons resultados com os sinais analisados. / This work has the purpose to analyze some techniques for myoelectric signal processing, towards a subsequent implementation of a circuit which can recognize this signal and present as output a control signal to be used in rehabilitation systems. Simulation and evaluation of three filtering techniques for the myoelectric signal were done in order to attenuate the main interferences of noises which corrupt this signal. The evaluated techniques were: classic digital filtering; adaptive noise cancelling and the signal reconstruction through the obtained components by the wavelet transform. A simplified system of pattern recognition for this signal also was implemented and analyzed, accomplished through an artificial neural network. The myoelectric signal itself was applied to the input instead of its characteristics obtained by mathematical processing. According to the results obtained the adaptive noise cancelling presented better results in comparison to the other filtering techniques. Despite not being adequate for filtering, the wavelet transform proved to be a powerful tool for signal analysis, by virtue of its multiresolution characteristics. The technique used to recognize the signal patterns has shown good results with the analyzed signals.

<p>Active vibration control to reduce vibrations and structure borne noise is considered using a powerful multi-disciplinary virtual design environment which enables control system design to be considered as an integral part of the overall vehicle design.</p><p>The main application studied is active automotive engine vibration isolation where, first, the potential of large frequency band multi-input multi-output H₂ feedback control is considered. Facilitated by the virtual environment, it is found necessary to take non-linear characteristics into account to achieve closed-loop stability.</p><p>A physical explanation to why receiver structure flexibility insignificantly affect the open and closed-loop characteristics in case of total force feedback in contrast to acceleration feedback is then given. In this context, the inherent differences between model order reduction by modal and by balanced truncation are being stressed.</p><p>Next, applying state-of-the-art algorithms for recursive parameter estimation, time-domain adaptive filtering is shown to lack sufficient tracking performance to deal with multiple spectral components of transient engine excitations corresponding to rapid car accelerations.</p><p>Finally, plant non-linearity as well as transient excitation are successfully handled using narrow band control based on feedback of disturbance states estimates. To deal with the non-linear characteristics, an approach to generate linear parameter varying descriptions of non-linear systems is proposed. Parameter dependent quadratic stability is assessed using a derived affine closed-loop system representation.</p><p>This thesis also considers actuator saturation induced limit cycles for observer-based state feedback control systems encountered when dealing with the active isolation application. It is stressed that the fundamental observer-based anti-windup technique could imply severely deteriorated closed-loop characteristics and even sustained oscillations. That is in the case when the observer is fed by the saturated control signal in contrast to the computed one. Based on piecewise affine system descriptions, analytical tools to conclude about limit cycles and exponential closed-loop stability are provided for the two observer implementations.</p>

Active vibration control to reduce vibrations and structure borne noise is considered using a powerful multi-disciplinary virtual design environment which enables control system design to be considered as an integral part of the overall vehicle design. The main application studied is active automotive engine vibration isolation where, first, the potential of large frequency band multi-input multi-output H2 feedback control is considered. Facilitated by the virtual environment, it is found necessary to take non-linear characteristics into account to achieve closed-loop stability. A physical explanation to why receiver structure flexibility insignificantly affect the open and closed-loop characteristics in case of total force feedback in contrast to acceleration feedback is then given. In this context, the inherent differences between model order reduction by modal and by balanced truncation are being stressed. Next, applying state-of-the-art algorithms for recursive parameter estimation, time-domain adaptive filtering is shown to lack sufficient tracking performance to deal with multiple spectral components of transient engine excitations corresponding to rapid car accelerations. Finally, plant non-linearity as well as transient excitation are successfully handled using narrow band control based on feedback of disturbance states estimates. To deal with the non-linear characteristics, an approach to generate linear parameter varying descriptions of non-linear systems is proposed. Parameter dependent quadratic stability is assessed using a derived affine closed-loop system representation. This thesis also considers actuator saturation induced limit cycles for observer-based state feedback control systems encountered when dealing with the active isolation application. It is stressed that the fundamental observer-based anti-windup technique could imply severely deteriorated closed-loop characteristics and even sustained oscillations. That is in the case when the observer is fed by the saturated control signal in contrast to the computed one. Based on piecewise affine system descriptions, analytical tools to conclude about limit cycles and exponential closed-loop stability are provided for the two observer implementations.

When computational resources are limited, especially multipliers, distributed arithmetic (DA) is used in lieu of the typical multiplier-based filtering structures. However, DA is not well suited for adaptive applications. The bottleneck is updating the memory table. Several attempts have been done to accelerate updating the memory, but at the expense of additional memory usage and of convergence speed. To develop an adaptive DA filter with an uncompromised convergence rate, the memory table must be fully updated. In this research, an efficient method for fully updating a DA memory table is proposed. The proposed update method is based on exploiting the temporal locality of the stored data and subexpression sharing. The proposed update method reduces the computational workload and requires no additional memory resources. DA using the proposed update method is called conjugate distributed arithmetic. Filters can also be constructed from analog components. Often, for lower precision computations, analog circuits use less power and less chip area than their digital counterparts. However, digital components are often used because of their ease of reprogrammability. Achieving such reprogrammability in analog is possible, but at the expense of additional chip area. A reprogrammable mixed-signal DA finite impulse response (FIR) filter is proposed to address the issues with reprogrammable analog FIR filters that are constructing compact reprogrammable filtering structures, non-symmetric and imprecise filter coefficients, inconsistent sampling of the input data, and input sample data corruption. These issues are successfully addressed using distributed arithmetic, digital registers, and epots. Also, a mixed-signal DA second-order section (SOS), which is used as the building block for higher order infinite impulse response filters, was proposed. The type of issues with an analog SOS filter are similar to those of an analog FIR filter, which are the lack of a compact reprogrammable filtering structure, the imprecise filter coefficients, the inconsistent sampling of the data, and the corruption of the data samples. These issues are successfully addressed using distributed arithmetic and digital registers.

With the current demand for mixed-signal SoCs, an increasing number of designers are looking for ADC architectures that can be easily implemented over digital substrates. Since ADC performance is strongly dependent upon physical and electrical features, it gets more difficult for them to benefit from more recent technologies, where these features are more variable. This way, analog signal acquisition is not allowed to follow an evolutionary trend compatible with Moore’s Law. In fact, such trend shall get worst, since newer technologies are expected to have more variable characteristics. Also, for a matter of economy of scale, many times a mixed-signal SoC presents a good amount of idle processing power. In such systems it is advantageous to employ more costly digital signal processing provided that it allows a reduction in the analog area demanded or the use of less expensive analog blocks, able to cope with process variations and uncertainty. Besides the technological concerns, other factors that impact the cost of the design also advise to transfer problems from the analog to the digital domain whenever possible: design automation and self-test requirements, for instance. Recent surveys indicate that the total cost in designer hours for the analog blocks of a mixed-signal system can be up to three times the cost of the digital ones. This manuscript explores the concept of bottom-up analog acquisition design, using statistical sampling as a way to reduce the analog area demanded in the design of ADCs within mixed-signal systems. More particularly, it investigates the possibility of using digital modeling and digital compensation of non-idealities to ease the design of ADCs. The work is developed around three axes: the definition of target applications, the development of digital compensation algorithms and the exploration of architectural possibilities. New methods and architectures are defined and validated. The main notions behind the proposal are analyzed and it is shown that the approach is feasible, opening new paths of future research. Keywords:

Orientador: Prof. Dr. Luiz Alberto Luz de Almeida / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Elétrica, 2017. / O motor de indução é a máquina elétrica de maior utilização em todo o planeta e seu desempenho é fundamental nos processos produtivos, fazendo se necessário o funcionamento livre de falhas. Baseado na análise da assinatura da corrente do motor (MCSA) é possível apontar falhas em motores de indução, como barras quebradas, através da análise de variações na corrente do estator, que no domínio da frequência geram bandas laterais à frequência fundamental. Porém, devido à dificuldade e alta complexidade para se lidar com a grande diferença entre as magnitudes das bandas laterais e a frequência fundamental, foi proposto na literatura uma técnica que atenua a componente da frequência fundamental via Transformada Recursiva Discreta de Fourier (RDFT) com objetivo de amplificar os espectros de bandas laterais gerados. Entretanto, a técnica proposta estima a componente fundamental baseando-se em uma frequência fixa (60Hz), sem considerar as oscilações presentes na rede que podem diretamente afetar o resultado da atenuação. É proposto neste trabalho uma filtragem adaptativa híbrida analógico-digital para melhoria na atenuação da componente fundamental através da implementação de um sistema compensador das oscilações da rede composto por um estimador de frequência do tipo "Zero-Crossing" e um oscilador controlado numericamente (NCO). Isto acarreta em baixa complexidade, aumentando a eficiência e confiabilidade do controle dos dados e acima de tudo levando em conta o contexto atual de redução de custos, permite a portabilidade para sistemas de baixo custo e Iot. / The induction motor is the most applied electrical machine around the planet and in its majority, plays a fundamental role in the productive process, requiring faults free functioning. Based on motor current signature analysis (MCSA) it is possible point faults in induction motors, as broken bars, through the analysis of the stators current imbalances, which in frequency domain generate sidebands around the fundamental frequency. Nevertheless, due the difficulty and the high complexity to handle the differences between the sidebands and fundamental frequency magnitudes, a technique which suppresses the fundamental frequency via Recursive Discrete Fourier Transform was proposed in order to amplify the sidebands spectrum generated. However, the proposed technique estimates the fundamental component based on a fixed frequency (60Hz), without considering the grid oscillations which can directly affect the result of the fundamental attenuation. It is proposed in this study a hybrid analogic-digital adaptive filtering in order to improve the fundamental component cancelling technique by implementing a grid oscillations compensator system composed by a Zero-Crossing Frequency Estimator and a Numerically Controlled Oscillator (NCO). It will result in low complexity, increasing the data control efficiency and reliability and above all taking in consideration the current reduction cost context, allow the portability to low cost and Iot systems.

With the current demand for mixed-signal SoCs, an increasing number of designers are looking for ADC architectures that can be easily implemented over digital substrates. Since ADC performance is strongly dependent upon physical and electrical features, it gets more difficult for them to benefit from more recent technologies, where these features are more variable. This way, analog signal acquisition is not allowed to follow an evolutionary trend compatible with Moore’s Law. In fact, such trend shall get worst, since newer technologies are expected to have more variable characteristics. Also, for a matter of economy of scale, many times a mixed-signal SoC presents a good amount of idle processing power. In such systems it is advantageous to employ more costly digital signal processing provided that it allows a reduction in the analog area demanded or the use of less expensive analog blocks, able to cope with process variations and uncertainty. Besides the technological concerns, other factors that impact the cost of the design also advise to transfer problems from the analog to the digital domain whenever possible: design automation and self-test requirements, for instance. Recent surveys indicate that the total cost in designer hours for the analog blocks of a mixed-signal system can be up to three times the cost of the digital ones. This manuscript explores the concept of bottom-up analog acquisition design, using statistical sampling as a way to reduce the analog area demanded in the design of ADCs within mixed-signal systems. More particularly, it investigates the possibility of using digital modeling and digital compensation of non-idealities to ease the design of ADCs. The work is developed around three axes: the definition of target applications, the development of digital compensation algorithms and the exploration of architectural possibilities. New methods and architectures are defined and validated. The main notions behind the proposal are analyzed and it is shown that the approach is feasible, opening new paths of future research. Keywords:

With the current demand for mixed-signal SoCs, an increasing number of designers are looking for ADC architectures that can be easily implemented over digital substrates. Since ADC performance is strongly dependent upon physical and electrical features, it gets more difficult for them to benefit from more recent technologies, where these features are more variable. This way, analog signal acquisition is not allowed to follow an evolutionary trend compatible with Moore’s Law. In fact, such trend shall get worst, since newer technologies are expected to have more variable characteristics. Also, for a matter of economy of scale, many times a mixed-signal SoC presents a good amount of idle processing power. In such systems it is advantageous to employ more costly digital signal processing provided that it allows a reduction in the analog area demanded or the use of less expensive analog blocks, able to cope with process variations and uncertainty. Besides the technological concerns, other factors that impact the cost of the design also advise to transfer problems from the analog to the digital domain whenever possible: design automation and self-test requirements, for instance. Recent surveys indicate that the total cost in designer hours for the analog blocks of a mixed-signal system can be up to three times the cost of the digital ones. This manuscript explores the concept of bottom-up analog acquisition design, using statistical sampling as a way to reduce the analog area demanded in the design of ADCs within mixed-signal systems. More particularly, it investigates the possibility of using digital modeling and digital compensation of non-idealities to ease the design of ADCs. The work is developed around three axes: the definition of target applications, the development of digital compensation algorithms and the exploration of architectural possibilities. New methods and architectures are defined and validated. The main notions behind the proposal are analyzed and it is shown that the approach is feasible, opening new paths of future research. Keywords: