Las técnicas de identificación permiten construir modelos matemáticos para sistemas dinámicos a partir de datos registrados de un experimento o del normal funcionamiento del sistema a modelar. El diseño de un modelo implica un compromiso entre su simplicidad y la necesidad de capturar los aspectos esenciales del sistema en estudio. Los modelos caja negra se diseñan enteramente a partir de los datos entrada/salida disponibles del sistema, sin tener en cuenta la interpretación de los parámetros que lo definen. Existen dife-rentes clases de modelos caja negra; considerando su mayor simplicidad, los primeros en desarrollarse fueron los modelos lineales. Posteriormente, dada la necesidad de modelar con mayor precisión, surgieron los modelos no lineales. Una de las principales clases de modelos no lineales de caja negra son los modelos tipo Wiener. Las estructuras que proponemos en esta tesis están dentro de esta familia de modelos. Presentamos, en primer lugar, una estructura de modelo basada en funcio-nes Canónicas Lineales a Tramos de Alto Nivel (CLATAN) y un algoritmo de identificación NOE (por sus siglas en inglés, Non-linear Output Error). Exploramos además la capacidad de apro-ximación, de generalización así como también la estabilidad de este modelo. El algoritmo propuesto permite comenzar con una aproximación OE y aumentar fácilmente el orden hasta al-canzar la aproximación deseada, conservando la aproximación lograda hasta el orden inmediato anterior. Por otra parte, el algoritmo de aprendizaje para determinar los parámetros ga-rantiza la BIBO estabilidad del modelo. Luego, proponemos dos esquemas de aproximación para los cuales probamos que per-miten aproximar cualquier sistema dinámico discreto, no lineal, causal, invariante en el tiempo y con memoria evanescente. Estos modelos están compuestos por un conjunto finito de sistemas discretos de Laguerre o de Kautz, relacionados de manera no lineal mediante funciones CLATAN, cuyos paráme-tros ajustamos utilizando teoría de estimación con conjuntos de membresía (teoría SM). Con esta metodología, estimamos dichos parámetros asumiendo sólo que el ruido es desconocido pero acotado en alguna norma dada (ruido UBB), lo que cons-tituye una hipótesis débil para el mismo. Por otra parte, me-diante la teoría SM hallamos un conjunto que contiene todas las posibles soluciones del problema, lo que nos permite es-timar las cotas de incertidumbre asociadas al problema de es-timación. La metodología resultante es robusta, en el sentido que el conjunto de datos utilizado para la identificación del sistema en estudio puede ser reproducido por al menos uno de los modelos en el conjunto de parámetros identificados. / System identification deals with mathematical models for dynamical systems built from gathered data from experi-ments. The design of such models implies a trade of between simplicity and the need to capture the essential features of the system under study. Black box models are based entirely upon the available input/output data, regar-dless of any interpretation of the parameters involved. Due to its simplicity, linear black box models were first developed. Later, on the urge for more accurate models led to the development of non-linear ones. Wiener like-models constitute one of the most relevant classes of non-linear models. The models proposed in this Thesis belong to this class.We first propose a model structure based on High Level Canonical Piecewise Linear(HLCPWL) functions and a Nonlinear Output Error (NOE) identification algorithm. We explore the approximation capabilities of this structure together with its generalization and stability properties. Starting from a linear Output Error (OE) approximation, this model family yields an identification algorithm such that the order of the model can be easily increased during the identification process, retaining the previously achie-ved approximation. The parameters of the HLCPWL functions arlearned using a simple algorithm that guarantees BIBO stability of the model. Next, we consider two approxima-tion schemes for non linear, discrete, causal, timeinva-riant dynamical systems with fading memory. In these mo-dels, the dynamic linear part is represented by a finite set of Laguerre or Kautz basis functions, while the non-linear static part is realized by High Level Canonical Piecewise Linear basis functions. We estimate the parame-ters of the HLCPWL functions using set membership estima-tion theory. This theory allows to estimate the models parameters under mild conditions for the noise; in fact we only assume that the noise is unknown but bounded (UBB). We also provide a methodology for estimating the uncer-tainty bounds for the models and prove that this structure allows to uniformly approximate any nonlinear discrete, causal, time-invariant systems with fading memory. The proposed methodology is robust, in the sense that the data set used for the identication of the system under study can be reproduced by at least one of the models within the set of all identified parameters.

The research in this dissertation addresses reduced rank adaptive signal processing, with specific emphasis on the multistage Wiener filter (MWF). The MWF is a generalization of the classical Wiener filter that performs a stage-by-stage decomposition based on orthogonal projections. Truncation of this decomposition produces a reduced rank filter with many benefits, for example, improved performance. This dissertation extends knowledge of the MWF in four areas. The first area is rank and sample support compression. This dissertation examines, under a wide variety of conditions, the size of the adaptive subspace required by the MWF (i.e., the rank) as well as the required number of training samples. Comparisons are made with other algorithms such as the eigenvector-based principal components algorithm. The second area investigated in this dissertation concerns "soft stops", i.e., the insertion of diagonal loading into the MWF. Several methods for inserting loading into the MWF are described, as well as methods for choosing the amount of loading. The next area investigated is MWF rank selection. The MWF will outperform the classical Wiener filter when the rank is properly chosen. This dissertation presents six approaches for selecting MWF rank. The algorithms are compared to one another and an overall design space taxonomy is presented. Finally, as digital modelling capabilities become more sophisticated there is emerging interest in augmenting adaptive processing algorithms to incorporate prior knowledge. This dissertation presents two methods for augmenting the MWF, one based on linear constraints and a second based on non-zero weight vector initialization. Both approaches are evaluated under ideal and perturbed conditions. Together the research described in this dissertation increases the utility and robustness of the multistage Wiener filter. The analysis is presented in the context of adaptive array processing, both spatial array processing and space-time adaptive processing for airborne radar. The results, however, are applicable across the entire spectrum of adaptive signal processing applications. / Ph. D.

Adaptive LMS equalizers are widely used in digital communication systems for their simplicity in implementation. Conventional adaptive filtering theory suggests the upper bound of the performance of such equalizer is determined by the performance of a Wiener filter of the same structure. However, in the presence of a narrowband interferer the performance of the LMS equalizer is better than that of its Wiener counterpart. This phenomenon, termed a non-Wiener effect, has been observed before and substantial work has been done in explaining the underlying reasons. In this work, we focus on the Bit Error Rate (BER) performance of LMS equalizers. At first a model “the Gaussian Mixture (GM) model“ is presented to estimate the BER performance of a Wiener filter operating in an environment dominated by a narrowband interferer. Simulation results show that the model predicts BER accurately for a wide range of SNR, ISR, and equalizer length. Next, a model similar to GM termed the Gaussian Mixture using Steady State Weights (GMSSW) model is proposed to model the BER behavior of the adaptive NLMS equalizer. Simulation results show unsatisfactory performance of the model. A detailed discussion is presented that points out the limitations of the GMSSW model, thereby providing some insight into the non-Wiener behavior of (N)LMS equalizers. An improved model, the Gaussian with Mean Square Error (GMSE), is then proposed. Simulation results show that the GMSE model is able to model the non-Wiener characteristics of the NLMS equalizer when the normalized step size is between 0 and 0.4. A brief discussion is provided on why the model is inaccurate for larger step sizes. / Master of Science

The blind source separation problem has received a great deal of attention in previous years. The aim of this problem is to estimate a set of original source signals from a set of linearly mixed signals through any number of signal processing techniques. While many methods exist that attempt to solve the blind source separation problem, a new technique is being used that uniquely separates audio sources as they are received from a microphone array. In this thesis a new algorithm is proposed that that utilizes the ICA algorithm in conjunction with a filtering technique that separates source signals and then removes sources of interference so that a signal of interest can be accurately tracked. Experimental results will compare a common blind source separation technique to the new algorithm and show that the new algorithm can detect a signal of interest and accurately track it as it moves through an anechoic environment. / Master of Science

We study the linear abstract kinetic equation T𝜑(x)′=-A𝜑(x) in the half space {x≥0} with partial range boundary conditions. The function <i>ψ</i> takes values in a Hilbert space H, T is a self adjoint injective operator on H and A is an accretive operator. The first step in the analysis of this boundary value problem is to show that T⁻¹A generates a holomorphic bisemigroup. We prove two theorems about perturbation of bisemigroups that are interesting in their own right. The second step is to obtain a special decomposition of H which is equivalent to a Wiener-Hopf factorization. The accretivity of A is crucial in this step. When A is of the form "identity plus a compact operator", we work in the original Hilbert space. For unbounded A’s we consider weak solutions in a larger space H_T, which has a natural Krein space structure. Using the Krein space geometry considerably simplifies the analysis of the question of unique solvability. / Ph. D. / incomplete_metadata

Adaptive Least Mean Square (LMS) equalizers are widely used in digital communication systems primarily for their ease of implementation and lack of dependence on a priori knowledge of input signal statistics. LMS equalizers exhibit non-Wiener characteristics in the presence of a strong narrowband interference and can outperform the optimal Wiener equalizer in terms of both mean square error (MSE) and bit error rate (BER). There has been significant work in the past related to the analysis of the non-Wiener characteristics of the LMS equalizer, which includes the discovery of the shift in the mean of the LMS weights from the corresponding Wiener weights and the modeling of steady state MSE performance. BER performance is ultimately a more practically relevant metric than MSE for characterizing system performance. The present work focuses on modeling the steady state BER performance of the normalized LMS (NLMS) equalizer operating in the presence of a strong narrowband interference. Initial observations showed that a 2 dB improvement in MSE may result in two orders of magnitude improvement in BER. However, some differences in the MSE and BER behavior of the NLMS equalizer were also seen, most notably the significant dependence (one order of magnitude variation) of the BER behavior on the interference frequency, a dependence not seen in MSE. Thus, MSE cannot be used as a predictor for the BER performance; the latter further motivates the pursuit of a separate BER model. The primary contribution of this work is the derivation of the probability density of the output of the NLMS equalizer conditioned on a particular symbol having been transmitted, which can then be leveraged to predict its BER performance. The analysis of the NLMS equalizer, operating in a strong narrowband interference environment, resulted in a conditional probability density function in the form of a Gaussian Sum Mixture (GSM). Simulation results verify the efficacy of the GSM expression for a wide range of system parameters, such as signal-to-noise ratio (SNR), interference-to-signal (ISR) ratio, interference frequency, and step-sizes over the range of mean-square stable operation of NLMS. Additionally, a low complexity approximate version of the GSM model is also derived and can be used to give a conservative lower bound on BER performance. A thorough analysis of the MSE and BER behavior of the Bi-scale NLMS equalizer (BNLMS), a variant of the NLMS equalizer, constitutes another important contribution of this work. Prior results indicated a 2 dB MSE improvement of BNLMS over NLMS in the presence of a strong narrowband interference. A closed form MSE model is derived for the BLMS algorithm. Additionally, BNLMS BER behavior was studied and showed the potential of two orders of magnitude improvement over NLMS. Analysis led to a BER model in the form of a GSM similar to the NLMS case but with different parameters. Simulation results verified that both models for MSE and BER provided accurate prediction of system performance for different combinations of SNR, ISR, interference frequency, and step-size. An enhanced GSM (EGSM) model to predict the BER performance for the NLMS equalizer is also introduced, specifically to address certain cases (low ISR cases) where the original GSM expression (derived for high ISR) was less accurate. Simulation results show that the EGSM model is more accurate in the low ISR region than the GSM expression. For the situations where the derived GSM expression was accurate, the BER estimates provided by the heuristic EGSM model coincided with those computed from the GSM expression. Finally, the two-interferer problem is introduced, where NLMS equalizer performance is studied in the presence of two narrowband interferers. Initial results show the presence of non-Wiener characteristics for the two-interferer case. Additionally, experimental results indicate that the BER performance of the NLMS equalizer operating in the presence of a single narrowband interferer may be improved by purposeful injection of a second narrowband interferer. / PHD / Every practical communication system requires effective interference mitigation schemes that are able to nullify unwanted signals without distorting the desired signal. Adaptive equalizers are among the prevalent systems used to cancel interfering signals. In particular, for narrowband interference (a particular class of interference) mitigation with (normalized) least mean square type (NLMS) equalizers has been found to be extremely effective. In fact, in the narrowband interference-dominated environment, NLMS equalizers have been found to work better than the solution with the same structure that is optimal according to linear filtering theory. This departure from the linear filtering theory is a result of the non-Wiener characteristics of NLMS type equalizers. This work investigates the bit error rate (BER) behavior, a common metric used to characterize the performance of wireless communication systems, of the NLMS equalizer in the presence of a strong narrowband interference. The major contribution of this dissertation is the derivation of an accurate expression that links the BER performance of the NLMS equalizer with the system parameters and signal statistics. Another variant of the NLMS equalizer known as the Bi-scale LMS (BLMS) equalizer was also studied. Similar to the NLMS case, an accurate BER expression for the BLMS equalizer was also derived. Additionally, situations were investigated where the non-Wiener characteristics of the NLMS equalizers can be leveraged. Overall, this dissertation hopes to add to the existing body of work that pertains to the analysis of non-Wiener effects of NLMS equalizers and thus, in general, to the work related to analysis of adaptive equalizers.

Neste trabalho, é apresentado um novo modelo de reconstrução tridimensional (3D) para amostras agrícolas com filtragem de Wiener em processamento paralelo, o qual é obtido a partir de reconstruções tomográficas bidimensionais (2D). No desenvolvimento, foram modelados algoritmos paralelos de retroprojeção filtrada e reconstrução tridimensional, baseando-se na inserção de um conjunto de planos virtuais entre pares de planos reais obtidos em ensaios tomográficos de raios X na faixa de energia de 56 keV a 662 keV. No modelo, os planos virtuais gerados em algoritmo paralelo são implementados com base na técnica de interpolação por B-Spline-Wavelet. Para validação do modelo desenvolvido, foi utilizada uma plataforma paralela composta de 4 processadores DSP, a qual possibilitou a troca de dados entre os processadores DSP e o envio de informações para o host, um computador desktop com processador Pentium III operando em 800 MHz. A extração de medidas de eficiência, de ganho e de precisão dos algoritmos paralelos foi realizada com base em um conjunto de amostras agrícolas (solo, vidro e madeiras) e de phantoms de calibração. Nessa avaliação, observou-se que o algoritmo de reconstrução 2D, utilizado como base para o algoritmo de reconstrução 3D, possibilitou uma alta eficiência para imagens de maior resolução, atingindo um pico de 92% de eficiência na resolução de 181X181 pixels. O algoritmo paralelo de reconstrução 3D foi analisado para um conjunto de amostras, sob diferentes configurações de planos reais e virtuais, organizados de forma a possibilitarem a avaliação do impacto causado pelo aumento da granularidade da comunicação e da carga de trabalho. Um melhor desempenho, com ganho médio igual a 3,4, foi obtido na reconstrução de objetos que demandaram o cálculo de um maior número de planos. Também, buscou-se conhecer a adaptabilidade do modelo para uso em arquitetura convencional, sendo que neste caso o uso de MPI permitiu a comunicação entre as tarefas projetadas em cada algoritmo paralelo. Adicionamente, foram incluídas ferramentas de visualização 2D e 3D para que usuários possam analisar as imagens e as características das amostras agrícolas em ambiente tridimensional. Os resultados obtidos indicam que o modelo de reconstrução 3D paralela trouxe contribuições originais para a área de tomografia agrícola aplicada à física de solos, bem como para a criação de ferramentas que viabilizem explorar recursos computacionais disponíveis em arquiteturas paralelas que demandem elevada capacidade de processamento. / This work presents a new method for three dimensional (3D) image reconstruction dedicated to the investigation in soil physics by means of X-ray tomography which is obtained using two-dimensional (2D) tomographic image reconstructed slices. The conception of the 3D model for reconstruction and visualization was based on the filtered back projection algorithm, operating under parallel environment together the insertion of virtual planes between pairs of real planes obtained by X-Ray tomography under energies varying from 56 keV to 662 keV. In this model, the virtual planes were generated by interpolation with the use of B-Spline-Wavelets. The evaluation of the 3D reconstruction model was established by using a set of agricultural samples (i.e., soil, glass, wood and calibration phantoms) having different configuration for the planes. Such configuration was based on setting not only the sizes and the number of the real but also the virtual planes in the volume. This procedure allows the impact measurements as a function of the increasing in workload and the communication granularity. To validate the reconstruction model, a dedicated parallel architecture composed of 4 DSP processors was used. This board enables data exchange between DSP processors and communication with host computer. A measurement of efficiency with a speed up equal to 3.4 was obtained using the same set of samples and a better performance was observed with a higher number of planes. Also, to understand about its adaptability, the model was implemented in conventional architecture, using MPI library to enable communication between designed tasks. Additionally, 2D and 3D visualization tools based on Vizualization ToolKit were included in order to help users to analyze images and their characteristics. Results have shown that the 3D parallel model reconstruction brought original contributions for the soil science diagnosis by X-Ray tomography, as well as to explore the available computational resources in parallel architectures, which demands great processing capacity.

Este trabalho tem por objetivo o desenvolvimento de uma nova técnica de pré-processamento de imagens mamográficas digitais para melhorar o desempenho dos esquemas computacionais de auxílio ao diagnóstico (CAD) e para auxiliar na detecção precoce do câncer de mama. O método proposto efetua uma restauração nas imagens mamográficas utilizando, em uma primeira etapa, a transformada de Anscombe e o filtro de Wiener para redução do ruído quântico. Posteriormente, é utilizado o filtro inverso da função de transferência de modulação (MTF) do sistema de imagem para realce das estruturas de interesse na mamografia, como as microcalcificações, que podem ser um indicativo de câncer de mama em seu estágio inicial. Imagens mamográficas restauradas pelo método proposto foram utilizadas na avaliação de um esquema CAD para detecção automática de microcalcificações. Os resultados mostraram que o desempenho do esquema CAD apresentou uma melhora significativa quando imagens restauradas foram utilizadas, mesmo para imagens de mamas densas, que resultam normalmente em baixa taxa de detecção devido ao baixo contraste. / This work aims to developing a new technique for pre-processing digital mammographic images in order to improve the performance of computer aided-diagnosis schemes (CAD) and to assist in early detection of breast cancer. The proposed method performs a restoration in mammographic images using in a first step, the Anscombe transform and Wiener filtering to reduce image quantum noise. Subsequently, it was used the inverse modulation transfer function filtering (MTF) considering the imaging system to enhance structures of interest in mammography, such as microcalcifications, which may be an indicative of breast cancer in its early stage. Mammographic images restored by the proposed method were used in the evaluation of a CAD scheme for automatic detection of microcalcifications. The results showed that the performance of the CAD scheme had a significant improvement when restored images were used, even for images of dense breasts, which often results in low detection rate due to low contrast.

Neste trabalho, é apresentado um novo modelo de reconstrução tridimensional (3D) para amostras agrícolas com filtragem de Wiener em processamento paralelo, o qual é obtido a partir de reconstruções tomográficas bidimensionais (2D). No desenvolvimento, foram modelados algoritmos paralelos de retroprojeção filtrada e reconstrução tridimensional, baseando-se na inserção de um conjunto de planos virtuais entre pares de planos reais obtidos em ensaios tomográficos de raios X na faixa de energia de 56 keV a 662 keV. No modelo, os planos virtuais gerados em algoritmo paralelo são implementados com base na técnica de interpolação por B-Spline-Wavelet. Para validação do modelo desenvolvido, foi utilizada uma plataforma paralela composta de 4 processadores DSP, a qual possibilitou a troca de dados entre os processadores DSP e o envio de informações para o host, um computador desktop com processador Pentium III operando em 800 MHz. A extração de medidas de eficiência, de ganho e de precisão dos algoritmos paralelos foi realizada com base em um conjunto de amostras agrícolas (solo, vidro e madeiras) e de phantoms de calibração. Nessa avaliação, observou-se que o algoritmo de reconstrução 2D, utilizado como base para o algoritmo de reconstrução 3D, possibilitou uma alta eficiência para imagens de maior resolução, atingindo um pico de 92% de eficiência na resolução de 181X181 pixels. O algoritmo paralelo de reconstrução 3D foi analisado para um conjunto de amostras, sob diferentes configurações de planos reais e virtuais, organizados de forma a possibilitarem a avaliação do impacto causado pelo aumento da granularidade da comunicação e da carga de trabalho. Um melhor desempenho, com ganho médio igual a 3,4, foi obtido na reconstrução de objetos que demandaram o cálculo de um maior número de planos. Também, buscou-se conhecer a adaptabilidade do modelo para uso em arquitetura convencional, sendo que neste caso o uso de MPI permitiu a comunicação entre as tarefas projetadas em cada algoritmo paralelo. Adicionamente, foram incluídas ferramentas de visualização 2D e 3D para que usuários possam analisar as imagens e as características das amostras agrícolas em ambiente tridimensional. Os resultados obtidos indicam que o modelo de reconstrução 3D paralela trouxe contribuições originais para a área de tomografia agrícola aplicada à física de solos, bem como para a criação de ferramentas que viabilizem explorar recursos computacionais disponíveis em arquiteturas paralelas que demandem elevada capacidade de processamento. / This work presents a new method for three dimensional (3D) image reconstruction dedicated to the investigation in soil physics by means of X-ray tomography which is obtained using two-dimensional (2D) tomographic image reconstructed slices. The conception of the 3D model for reconstruction and visualization was based on the filtered back projection algorithm, operating under parallel environment together the insertion of virtual planes between pairs of real planes obtained by X-Ray tomography under energies varying from 56 keV to 662 keV. In this model, the virtual planes were generated by interpolation with the use of B-Spline-Wavelets. The evaluation of the 3D reconstruction model was established by using a set of agricultural samples (i.e., soil, glass, wood and calibration phantoms) having different configuration for the planes. Such configuration was based on setting not only the sizes and the number of the real but also the virtual planes in the volume. This procedure allows the impact measurements as a function of the increasing in workload and the communication granularity. To validate the reconstruction model, a dedicated parallel architecture composed of 4 DSP processors was used. This board enables data exchange between DSP processors and communication with host computer. A measurement of efficiency with a speed up equal to 3.4 was obtained using the same set of samples and a better performance was observed with a higher number of planes. Also, to understand about its adaptability, the model was implemented in conventional architecture, using MPI library to enable communication between designed tasks. Additionally, 2D and 3D visualization tools based on Vizualization ToolKit were included in order to help users to analyze images and their characteristics. Results have shown that the 3D parallel model reconstruction brought original contributions for the soil science diagnosis by X-Ray tomography, as well as to explore the available computational resources in parallel architectures, which demands great processing capacity.

Este trabalho tem por objetivo o desenvolvimento de uma nova técnica de pré-processamento de imagens mamográficas digitais para melhorar o desempenho dos esquemas computacionais de auxílio ao diagnóstico (CAD) e para auxiliar na detecção precoce do câncer de mama. O método proposto efetua uma restauração nas imagens mamográficas utilizando, em uma primeira etapa, a transformada de Anscombe e o filtro de Wiener para redução do ruído quântico. Posteriormente, é utilizado o filtro inverso da função de transferência de modulação (MTF) do sistema de imagem para realce das estruturas de interesse na mamografia, como as microcalcificações, que podem ser um indicativo de câncer de mama em seu estágio inicial. Imagens mamográficas restauradas pelo método proposto foram utilizadas na avaliação de um esquema CAD para detecção automática de microcalcificações. Os resultados mostraram que o desempenho do esquema CAD apresentou uma melhora significativa quando imagens restauradas foram utilizadas, mesmo para imagens de mamas densas, que resultam normalmente em baixa taxa de detecção devido ao baixo contraste. / This work aims to developing a new technique for pre-processing digital mammographic images in order to improve the performance of computer aided-diagnosis schemes (CAD) and to assist in early detection of breast cancer. The proposed method performs a restoration in mammographic images using in a first step, the Anscombe transform and Wiener filtering to reduce image quantum noise. Subsequently, it was used the inverse modulation transfer function filtering (MTF) considering the imaging system to enhance structures of interest in mammography, such as microcalcifications, which may be an indicative of breast cancer in its early stage. Mammographic images restored by the proposed method were used in the evaluation of a CAD scheme for automatic detection of microcalcifications. The results showed that the performance of the CAD scheme had a significant improvement when restored images were used, even for images of dense breasts, which often results in low detection rate due to low contrast.