Avaliação do efeito de janela e descoloração nos filtros Wiener-Hopf

A presente dissertação consta de estudos sobre deconvolução sísmica, onde buscamos otimizar desempenhos na operação de suavização, na resolução da estimativa da distribuição dos coeficientes de reflexão e na recuperação do pulso-fonte. Os filtros estudados são monocanais, e as formulações consideram o sismograma como o resultado de um processo estocástico estacionário, e onde demonstramos os efeitos de janelas e de descoloração. O principio aplicado é o da minimização da variância dos desvios entre o valor obtido e o desejado, resultando no sistema de equações normais Wiener-Hopf cuja solução é o vetor dos coeficientes do filtro para ser aplicado numa convolução. O filtro de deconvolução ao impulso é desenhado considerando a distribuição dos coeficientes de reflexão como uma série branca. O operador comprime bem os eventos sísmicos a impulsos, e o seu inverso é uma boa aproximação do pulso-fonte. O janelamento e a descoloração melhoram o resultado deste filtro. O filtro de deconvolução aos impulsos é desenhado utilizando a distribuição dos coeficientes de reflexão. As propriedades estatísticas da distribuição dos coeficientes de reflexão tem efeito no operador e em seu desempenho. Janela na autocorrelação degrada a saída, e a melhora é obtida quando ela é aplicada no operador deconvolucional. A transformada de Hilbert não segue o princípio dos mínimos-quadrados, e produz bons resultados na recuperação do pulso-fonte sob a premissa de fase-mínima. O inverso do pulso-fonte recuperado comprime bem os eventos sísmicos a impulsos. Quando o traço contém ruído aditivo, os resultados obtidos com auxilio da transformada de Hilbert são melhores do que os obtidos com o filtro de deconvolução ao impulso. O filtro de suavização suprime ruído presente no traço sísmico em função da magnitude do parâmetro de descoloração utilizado. A utilização dos traços suavizados melhora o desempenho da deconvolução ao impulso. A descoloração dupla gera melhores resultados do que a descoloração simples. O filtro casado é obtido através da maximização de uma função sinal/ruído. Os resultados obtidos na estimativa da distribuição dos coeficientes de reflexão com o filtro casado possuem melhor resolução do que o filtro de suavização.

Fault detection in rotating machines by vibration signal processing techniques

Machines with moving parts give rise to vibrations and consequently noise. The setting up and the status of each machine yield to a peculiar vibration signature. Therefore, a change in the vibration signature, due to a change in the machine state, can be used to detect incipient defects before they become critical. This is the goal of condition monitoring, in which the informations obtained from a machine signature are used in order to detect faults at an early stage. There are a large number of signal processing techniques that can be used in order to extract interesting information from a measured vibration signal. This study seeks to detect rotating machine defects using a range of techniques including synchronous time averaging, Hilbert transform-based demodulation, continuous wavelet transform, Wigner-Ville distribution and spectral correlation density function. The detection and the diagnostic capability of these techniques are discussed and compared on the basis of experimental results concerning gear tooth faults, i.e. fatigue crack at the tooth root and tooth spalls of different sizes, as well as assembly faults in diesel engine. Moreover, the sensitivity to fault severity is assessed by the application of these signal processing techniques to gear tooth faults of different sizes.

Ground penetrating radar early-time technique for soil electromagnetic parameters estimation

In recent years, thanks to the technological advances, electromagnetic methods for non-invasive shallow subsurface characterization have been increasingly used in many areas of environmental and geoscience applications. Among all the geophysical electromagnetic methods, the Ground Penetrating Radar (GPR) has received unprecedented attention over the last few decades due to its capability to obtain, spatially and temporally, high-resolution electromagnetic parameter information thanks to its versatility, its handling, its non-invasive nature, its high resolving power, and its fast implementation. The main focus of this thesis is to perform a dielectric site characterization in an efficient and accurate way studying in-depth a physical phenomenon behind a recent developed GPR approach, the so-called early-time technique, which infers the electrical properties of the soil in the proximity of the antennas. In particular, the early-time approach is based on the amplitude analysis of the early-time portion of the GPR waveform using a fixed-offset ground-coupled antenna configuration where the separation between the transmitting and receiving antenna is on the order of the dominant pulse-wavelength. Amplitude information can be extracted from the early-time signal through complex trace analysis, computing the instantaneous-amplitude attributes over a selected time-duration of the early-time signal. Basically, if the acquired GPR signals are considered to represent the real part of a complex trace, and the imaginary part is the quadrature component obtained by applying a Hilbert transform to the GPR trace, the amplitude envelope is the absolute value of the resulting complex trace (also known as the instantaneous-amplitude). Analysing laboratory information, numerical simulations and natural field conditions, and summarising the overall results embodied in this thesis, it is possible to suggest the early-time GPR technique as an effective method to estimate physical properties of the soil in a fast and non-invasive way.

Análisis de sistemas dinámicos y complejos en la Liga Profesional de Balonmano de España = Complex and dynamical systems analysis in Spanish Professional Handball League

El propósito de esta tesis fue estudiar el rendimiento ofensivo de los equipos de balonmano de élite cuando se considera el balonmano como un sistema dinámico complejo no lineal. La perspectiva de análisis dinámica dependiente del tiempo fue adoptada para evaluar el rendimiento de los equipos durante el partido. La muestra general comprendió los 240 partidos jugados en la temporada 2011-2012 de la liga profesional masculina de balonmano de España (Liga ASOBAL). En el análisis posterior solo se consideraron los partidos ajustados (diferencia final de goles ≤ 5; n = 142). El estado del marcador, la localización del partido, el nivel de los oponentes y el periodo de juego fueron incorporados al análisis como variables situacionales. Tres estudios compusieron el núcleo de la tesis. En el primer estudio, analizamos la coordinación entre las series temporales que representan el proceso goleador a lo largo del partido de cada uno de los dos equipos que se enfrentan. Autocorrelaciones, correlaciones cruzadas, doble media móvil y transformada de Hilbert fueron usadas para el análisis. El proceso goleador de los equipos presentó una alta consistencia a lo largo de todos los partidos, así como fuertes modos de coordinación en fase en todos los contextos de juego. Las únicas diferencias se encontraron en relación al periodo de juego. La coordinación en los procesos goleadores de los equipos fue significativamente menor en el 1er y 2º periodo (0–10 min y 10–20 min), mostrando una clara coordinación creciente a medida que el partido avanzaba. Esto sugiere que son los 20 primeros minutos aquellos que rompen los partidos. En el segundo estudio, analizamos los efectos temporales (efecto inmediato, a corto y a medio plazo) de los tiempos muertos en el rendimiento goleador de los equipos. Modelos de regresión lineal múltiple fueron empleados para el análisis. Los resultados mostraron incrementos de 0.59, 1.40 y 1.85 goles para los periodos que comprenden la primera, tercera y quinta posesión de los equipos que pidieron el tiempo muerto. Inversamente, se encontraron efectos significativamente negativos para los equipos rivales, con decrementos de 0.50, 1.43 y 2.05 goles en los mismos periodos respectivamente. La influencia de las variables situacionales solo se registró en ciertos periodos de juego. Finalmente, en el tercer estudio, analizamos los efectos temporales de las exclusiones de los jugadores sobre el rendimiento goleador de los equipos, tanto para los equipos que sufren la exclusión (inferioridad numérica) como para los rivales (superioridad numérica). Se emplearon modelos de regresión lineal múltiple para el análisis. Los resultados mostraron efectos negativos significativos en el número de goles marcados por los equipos con un jugador menos, con decrementos de 0.25, 0.40, 0.61, 0.62 y 0.57 goles para los periodos que comprenden el primer, segundo, tercer, cuarto y quinto minutos previos y posteriores a la exclusión. Para los rivales, los resultados mostraron efectos positivos significativos, con incrementos de la misma magnitud en los mismos periodos. Esta tendencia no se vio afectada por el estado del marcador, localización del partido, nivel de los oponentes o periodo de juego. Los incrementos goleadores fueron menores de lo que se podría esperar de una superioridad numérica de 2 minutos. Diferentes teorías psicológicas como la paralización ante situaciones de presión donde se espera un gran rendimiento pueden ayudar a explicar este hecho. Los últimos capítulos de la tesis enumeran las conclusiones principales y presentan diferentes aplicaciones prácticas que surgen de los tres estudios. Por último, se presentan las limitaciones y futuras líneas de investigación. ABSTRACT The purpose of this thesis was to investigate the offensive performance of elite handball teams when considering handball as a complex non-linear dynamical system. The time-dependent dynamic approach was adopted to assess teams’ performance during the game. The overall sample comprised the 240 games played in the season 2011-2012 of men’s Spanish Professional Handball League (ASOBAL League). In the subsequent analyses, only close games (final goal-difference ≤ 5; n = 142) were considered. Match status, game location, quality of opposition, and game period situational variables were incorporated into the analysis. Three studies composed the core of the thesis. In the first study, we analyzed the game-scoring coordination between the time series representing the scoring processes of the two opposing teams throughout the game. Autocorrelation, cross-correlation, double moving average, and Hilbert transform were used for analysis. The scoring processes of the teams presented a high consistency across all the games as well as strong in-phase modes of coordination in all the game contexts. The only differences were found when controlling for the game period. The coordination in the scoring processes of the teams was significantly lower for the 1st and 2nd period (0–10 min and 10–20 min), showing a clear increasing coordination behavior as the game progressed. This suggests that the first 20 minutes are those that break the game-scoring. In the second study, we analyzed the temporal effects (immediate effect, short-term effect, and medium-term effect) of team timeouts on teams’ scoring performance. Multiple linear regression models were used for the analysis. The results showed increments of 0.59, 1.40 and 1.85 goals for the periods within the first, third and fifth timeout ball possessions for the teams that requested the timeout. Conversely, significant negative effects on goals scored were found for the opponent teams, with decrements of 0.59, 1.43 and 2.04 goals for the same periods, respectively. The influence of situational variables on the scoring performance was only registered in certain game periods. Finally, in the third study, we analyzed the players’ exclusions temporal effects on teams’ scoring performance, for the teams that suffer the exclusion (numerical inferiority) and for the opponents (numerical superiority). Multiple linear regression models were used for the analysis. The results showed significant negative effects on the number of goals scored for the teams with one less player, with decrements of 0.25, 0.40, 0.61, 0.62, and 0.57 goals for the periods within the previous and post one, two, three, four and five minutes of play. For the opponent teams, the results showed positive effects, with increments of the same magnitude in the same game periods. This trend was not affected by match status, game location, quality of opposition, or game period. The scoring increments were smaller than might be expected from a 2-minute numerical playing superiority. Psychological theories such as choking under pressure situations where good performance is expected could contribute to explain this finding. The final chapters of the thesis enumerate the main conclusions and underline the main practical applications that arise from the three studies. Lastly, limitations and future research directions are described.

A general linear model for MEG beamformer imaging

A new general linear model (GLM) beamformer method is described for processing magnetoencephalography (MEG) data. A standard nonlinear beamformer is used to determine the time course of neuronal activation for each point in a predefined source space. A Hilbert transform gives the envelope of oscillatory activity at each location in any chosen frequency band (not necessary in the case of sustained (DC) fields), enabling the general linear model to be applied and a volumetric T statistic image to be determined. The new method is illustrated by a two-source simulation (sustained field and 20 Hz) and is shown to provide accurate localization. The method is also shown to locate accurately the increasing and decreasing gamma activities to the temporal and frontal lobes, respectively, in the case of a scintillating scotoma. The new method brings the advantages of the general linear model to the analysis of MEG data and should prove useful for the localization of changing patterns of activity across all frequency ranges including DC (sustained fields). © 2004 Elsevier Inc. All rights reserved.

Flat-top pulse generation based on a fiber Bragg grating in transmission

We propose and analyze a flat-top pulse generator based on a fiber Bragg grating (FBG) in transmission. As is shown in the examples, a uniform period FBG properly designed can exhibit a spectral response in transmission close to sinc function (in amplitude and phase) in a certain bandwidth, because of the logarithm Hilbert transform relations, which can be used to reshape a Gaussian-like input pulse into a flat-top pulse.

First order optical differentiator based on an FBG in transmission

Optical differentiators constitute a basic device for analog all-optical signal processing [1]. Fiber grating approaches, both fiber Bragg grating (FBG) and long period grating (LPG), constitute an attractive solution because of their low cost, low insertion losses, and full compatibility with fiber optic systems. A first order differentiator LPG approach was proposed and demonstrated in [2], but FBGs may be preferred in applications with a bandwidth up to few nm because of the extreme sensitivity of LPGs to environmental fluctuations [3]. Several FBG approaches have been proposed in [3-6], requiring one or more additional optical elements to create a first-order differentiator. A very simple, single optical element FBG approach was proposed in [7] for first order differentiation, applying the well-known logarithmic Hilbert transform relation of the amplitude and phase of an FBG in transmission [8]. Using this relationship in the design process, it was theoretically and numerically demonstrated that a single FBG in transmission can be designed to simultaneously approach the amplitude and phase of a first-order differentiator spectral response, without need of any additional elements. © 2013 IEEE.

Analysis Methodology for Vortex-Induced Motion (VIM) of a Monocolumn Platform Applying the Hilbert-Huang Transform Method

Vortex-induced motion (VIM) is a highly nonlinear dynamic phenomenon. Usual spectral analysis methods, using the Fourier transform, rely on the hypotheses of linear and stationary dynamics. A method to treat nonstationary signals that emerge from nonlinear systems is denoted Hilbert-Huang transform (HHT) method. The development of an analysis methodology to study the VIM of a monocolumn production, storage, and offloading system using HHT is presented. The purposes of the present methodology are to improve the statistics analysis of VIM. The results showed to be comparable to results obtained from a traditional analysis (mean of the 10% highest peaks) particularly for the motions in the transverse direction, although the difference between the results from the traditional analysis for the motions in the in-line direction showed a difference of around 25%. The results from the HHT analysis are more reliable than the traditional ones, owing to the larger number of points to calculate the statistics characteristics. These results may be used to design risers and mooring lines, as well as to obtain VIM parameters to calibrate numerical predictions. [DOI: 10.1115/1.4003493]

Counterexamples to some pointwise estimates of the maximal Cauchy transform in terms of the Cauchy transform

Motivated by the work of Mateu, Orobitg, Pérez and Verdera, who proved inequalities of the form $T_*f\lesssim M(Tf)$ or $T_*f\lesssim M^2(Tf)$ for certain singular integral operators $T$, such as the Hilbert or the Beurling transforms, we study the possibility of establishing this type of control for the Cauchy transform along a Lipschitz graph. We show that this is not possible in general, and we give a partial positive result when the graph is substituted by a Jordan curve.

The application of the Hilbert spectrum to the analysis of electromyographic signals

This paper investigates the application of the Hilbert spectrum (HS), which is a recent tool for the analysis of nonlinear and nonstationary time-series, to the study of electromyographic (EMG) signals. The HS allows for the visualization of the energy of signals through a joint time-frequency representation. In this work we illustrate the use of the HS in two distinct applications. The first is for feature extraction from EMG signals. Our results showed that the instantaneous mean frequency (IMNF) estimated from the HS is a relevant feature to clinical practice. We found that the median of the IMNF reduces when the force level of the muscle contraction increases. In the second application we investigated the use of the HS for detection of motor unit action potentials (MUAPs). The detection of MUAPs is a basic step in EMG decomposition tools, which provide relevant information about the neuromuscular system through the morphology and firing time of MUAPs. We compared, visually, how MUAP activity is perceived on the HS with visualizations provided by some traditional (e.g. scalogram, spectrogram, Wigner-Ville) time-frequency distributions. Furthermore, an alternative visualization to the HS, for detection of MUAPs, is proposed and compared to a similar approach based on the continuous wavelet transform (CWT). Our results showed that both the proposed technique and the CWT allowed for a clear visualization of MUAP activity on the time-frequency distributions, whereas results obtained with the HS were the most difficult to interpret as they were extremely affected by spurious energy activity. (c) 2008 Elsevier Inc. All rights reserved.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Irreducibility of Random Hilbert Schemes

We prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the set of nonempty Hilbert schemes as a probability space, we transform this set into a disjoint union of infinite binary trees, reinterpreting Macaulay's classification of admissible Hilbert polynomials. Choosing discrete probability distributions with infinite support on the trees establishes our notion of random Hilbert schemes. To bound the probability that random Hilbert schemes are irreducible and nonsingular, we show that at least half of the vertices in the binary trees correspond to Hilbert schemes with unique Borel-fixed points.

Analysis Of The Dna Fourier Transform-infrared Microspectroscopic Signature Using An All-reflecting Objective.

The Fourier transform-infrared (FT-IR) signature of dry samples of DNA and DNA-polypeptide complexes, as studied by IR microspectroscopy using a diamond attenuated total reflection (ATR) objective, has revealed important discriminatory characteristics relative to the PO2(-) vibrational stretchings. However, DNA IR marks that provide information on the sample's richness in hydrogen bonds have not been resolved in the spectral profiles obtained with this objective. Here we investigated the performance of an all reflecting objective (ARO) for analysis of the FT-IR signal of hydrogen bonds in DNA samples differing in base richness types (salmon testis vs calf thymus). The results obtained using the ARO indicate prominent band peaks at the spectral region representative of the vibration of nitrogenous base hydrogen bonds and of NH and NH2 groups. The band areas at this spectral region differ in agreement with the DNA base richness type when using the ARO. A peak assigned to adenine was more evident in the AT-rich salmon DNA using either the ARO or the ATR objective. It is concluded that, for the discrimination of DNA IR hydrogen bond vibrations associated with varying base type proportions, the use of an ARO is recommended.