Numerical methods for calculating poles of the scattering matrix with applications in grating theory

Waveguide and resonant properties of diffractive structures are often explained through the complex poles of their scattering matrices. Numerical methods for calculating poles of the scattering matrix with applications in grating theory are discussed. A new iterative method for computing the matrix poles is proposed. The method takes account of the scattering matrix form in the pole vicinity and relies upon solving matrix equations with use of matrix decompositions. Using the same mathematical approach, we also describe a Cauchy-integral-based method that allows all the poles in a specified domain to be calculated. Calculation of the modes of a metal-dielectric diffraction grating shows that the iterative method proposed has the high rate of convergence and is numerically stable for large-dimension scattering matrices. An important advantage of the proposed method is that it usually converges to the nearest pole.Comment: 9 pages, 2 figures, 4 table

Matrix pencil method for vital sign detection from signals acquired by microwave sensors

Microwave sensors have recently been introduced as high-temporal resolution sensors, which could be used in the contactless monitoring of artery pulsation and breathing. However, accurate and efficient signal processing methods are still required. In this paper, the matrix pencil method (MPM), as an efficient method with good frequency resolution, is applied to back-reflected microwave signals to extract vital signs. It is shown that decomposing of the signal to its damping exponentials fulfilled by MPM gives the opportunity to separate signals, e.g., breathing and heartbeat, with high precision. A publicly online dataset (GUARDIAN), obtained by a continuous wave microwave sensor, is applied to evaluate the performance of MPM. Two methods of bandpass filtering (BPF) and variational mode decomposition (VMD) are also implemented. In addition to the GUARDIAN dataset, these methods are also applied to signals acquired by an ultra-wideband (UWB) sensor. It is concluded that when the vital sign is sufficiently strong and pure, all methods, e.g., MPM, VMD, and BPF, are appropriate for vital sign monitoring. However, in noisy cases, MPM has better performance. Therefore, for non-contact microwave vital sign monitoring, which is usually subject to noisy situations, MPM is a powerful method

A Comparative Evaluation of four Algorithms for Numeric Solution of the Deconvolution on Unidimensional Systems

The present paper presents the comparison of a deconvolution algorithm with other three classical approaches for one-dimensional deconvolution of signals. The algorithm was proposed at the digital signal processing laboratory at UAZ. During the last three decades, the development of new ideas on the solution about deconvolution or n-dimensional signal restoration methods, have become to a new meaning to this problem, the idea remains the same since the 50’s in the engineering literature, that is “ signal restoration or approximation to it's original form with the purpose of a better analysis ”. When a signal x(t) is generated, the only way to be picked up is by a sensor. During the sensing process the convolution of x(t) with another type of signals occurs. Then, a new signal is generated by the convolution of x(t) with a function h(t) and other noisy components. To obtain the original signal x(t), we have an inverse problem and the solution will deliver an estimation of x(t) or x_hat(t). The final purpose of this work is to evaluate and classify the signal restoration capacity of each method.En el presente trabajo se presenta la comparación de un algoritmo de deconvolución con respecto de otros tres algoritmos clásicos utilizados para deconvolución unidimensional de señales. El algoritmo fue propuesto y analizado en el laboratorio de procesamiento digital de señales de la UAZ. Durante las últimas tres décadas se han desarrollado nuevas ideas sobre soluciones a problemas de deconvolución o restauración de señales n-dimensiónales, la idea sigue siendo la misma que se plantea en la literatura de la ingeniería que data de los años 50s "restaurar señales o aproximarlas a su forma original para realizar un análisis de las mismas con errores relativamente pequeños". Cuando una señal x(t) se origina tiene que pasar por algún medio para poder ser captada, durante este proceso se realiza una operación llamada convolución entre x(t) y otro tipo de señales, en el momento en que captamos la señal, ésta ya no es x(t) sino la convolución de x(t) con una función h(t) mas componentes de ruido existentes en el medio. Para obtener la señal x(t) es necesario resolver un problema inverso el cual al final nos proporciona una estimación de x(t) o x_hat(t). El propósito final del trabajo es evaluar y clasificar la capacidad de restauración de señales de cada uno de los cuatro métodos

High-resolution sinusoidal analysis for resolving harmonic collisions in music audio signal processing

Many music signals can largely be considered an additive combination of multiple sources, such as musical instruments or voice. If the musical sources are pitched instruments, the spectra they produce are predominantly harmonic, and are thus well suited to an additive sinusoidal model. However, due to resolution limits inherent in time-frequency analyses, when the harmonics of multiple sources occupy equivalent time-frequency regions, their individual properties are additively combined in the time-frequency representation of the mixed signal. Any such time-frequency point in a mixture where multiple harmonics overlap produces a single observation from which the contributions owed to each of the individual harmonics cannot be trivially deduced. These overlaps are referred to as overlapping partials or harmonic collisions. If one wishes to infer some information about individual sources in music mixtures, the information carried in regions where collided harmonics exist becomes unreliable due to interference from other sources. This interference has ramifications in a variety of music signal processing applications such as multiple fundamental frequency estimation, source separation, and instrumentation identification. This thesis addresses harmonic collisions in music signal processing applications. As a solution to the harmonic collision problem, a class of signal subspace-based high-resolution sinusoidal parameter estimators is explored. Specifically, the direct matrix pencil method, or equivalently, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) method, is used with the goal of producing estimates of the salient parameters of individual harmonics that occupy equivalent time-frequency regions. This estimation method is adapted here to be applicable to time-varying signals such as musical audio. While high-resolution methods have been previously explored in the context of music signal processing, previous work has not addressed whether or not such methods truly produce high-resolution sinusoidal parameter estimates in real-world music audio signals. Therefore, this thesis answers the question of whether high-resolution sinusoidal parameter estimators are really high-resolution for real music signals. This work directly explores the capabilities of this form of sinusoidal parameter estimation to resolve collided harmonics. The capabilities of this analysis method are also explored in the context of music signal processing applications. Potential benefits of high-resolution sinusoidal analysis are examined in experiments involving multiple fundamental frequency estimation and audio source separation. This work shows that there are indeed benefits to high-resolution sinusoidal analysis in music signal processing applications, especially when compared to methods that produce sinusoidal parameter estimates based on more traditional time-frequency representations. The benefits of this form of sinusoidal analysis are made most evident in multiple fundamental frequency estimation applications, where substantial performance gains are seen. High-resolution analysis in the context of computational auditory scene analysis-based source separation shows similar performance to existing comparable methods

Análise teórica e experimental do processo de medição in situ da impedância acústica

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, Florianópolis, 2011A medição in situ da impedância acústica possui uma série de vantagens em relação à medição da impedância em tubo de impedância e à medição do coeficiente de absorção em câmara reverberante. Entre essas vantagens, destacam-se o fato de a medição in situ ser um método não destrutivo e que leva em conta condições realistas de montagem da amostra, os efeitos de acúmulo de sujeira e a não necessidade de um ambiente especial para a medição. Entre os métodos de medição in situ mais comumente usados, destaca-se a técnica baseada na medição da função de transferência entre dois microfones (PP), posicionados próximos à amostra. As principais desvantagens desse método são suas limitações em baixas e altas frequências, devido à distância finita entre os microfones. A sonda PU, que integra um sensor de pressão (microfone) e um de velocidade de partícula não sofre essa limitação já que os dois sensores ocupam aproximadamente a mesma posição no espaço. A medição in situ requer, no entanto, devido à complexidade física do problema, a modelagem precisa do campo acústico em frente à amostra que se deseja caracterizar, especialmente porque em aplicações típicas a fonte sonora e a sonda PU estão próximas uma da outra e não se pode considerar que o campo acústico seja composto por ondas planas. A influência do algoritmo de dedução da impedância de superfície é a primeira fronteira explorada neste trabalho. A partir da escolha do melhor método de dedução da impedância de superfície, uma estimativa da incerteza de medição foi feita através do método de Monte Carlo. E já que as aplicações da técnica PU se destinam à medição de amostras de dimensões tipicamente limitadas, a influência do tamanho da amostra é investigada com um modelo em elemento de contorno (BEM) da medição. Após a verificação de que os resultados experimentais corroboram o modelo numérico, a influência de vários parâmetros em relação ao tamanho finito da amostra foi investigada e estratégias propostas para minimizar o erro encontrado. Como a principal estratégia de dedução da impedância de superfície se destina à medição de amostras localmente reativas, a medição de amostras não-localmente reativas também foi avaliada. Neste caso, um modelo analítico foi utilizado para simular a medição in situ com boa concordância em relação aos dados experimentais. Para amostras que não podem ser consideradas como localmente reativas, dois novos algoritmos de dedução foram propostos. O primeiro baseia-se na minimização do erro da resposta em frequência, usado com sucesso em diversos casos, e o segundo em mínimos quadrados, que se mostrou menos robusto. Finalmente a técnica PU foi contrastada com a técnica PP em algumas condições de medição in situ realistas, o que permitiu estabelecer algumas das vantagens e desvantagens de ambas