Análise wavelet e modelo de manchas em curvas de luz estelares dos telescópios espaciais Kepler e CoRoT

Analogous to sunspots and solar photospheric faculae, which visibility is modulated by stellar rotation, stellar active regions consist of cool spots and bright faculae caused by the magnetic field of the star. Such starspots are now well established as major tracers used to estimate the stellar rotation period, but their dynamic behavior may also be used to analyze other relevant phenomena such as the presence of magnetic activity and its cycles. To calculate the stellar rotation period, identify the presence of active regions and investigate if the star exhibits or not differential rotation, we apply two methods: a wavelet analysis and a spot model. The wavelet procedure is also applied here to study pulsation in order to identify specific signatures of this particular stellar variability for different types of pulsating variable stars. The wavelet transform has been used as a powerful tool for treating several problems in astrophysics. In this work, we show that the time-frequency analysis of stellar light curves using the wavelet transform is a practical tool for identifying rotation, magnetic activity, and pulsation signatures. We present the wavelet spectral composition and multiscale variations of the time series for four classes of stars: targets dominated by magnetic activity, stars with transiting planets, those with binary transits, and pulsating stars. We applied the Morlet wavelet (6th order), which offers high time and frequency resolution. By applying the wavelet transform to the signal, we obtain the wavelet local and global power spectra. The first is interpreted as energy distribution of the signal in time-frequency space, and the second is obtained by time integration of the local map. Since the wavelet transform is a useful mathematical tool for nonstationary signals, this technique applied to Kepler and CoRoT light curves allows us to clearly identify particular signatures for different phenomena. In particular, patterns were identified for the temporal evolution of the rotation period and other periodicity due to active regions affecting these light curves. In addition, a beat-pattern vii signature in the local wavelet map of pulsating stars over the entire time span was also detected. The second method is based on starspots detection during transits of an extrasolar planet orbiting its host star. As a planet eclipses its parent star, we can detect physical phenomena on the surface of the star. If a dark spot on the disk of the star is partially or totally eclipsed, the integrated stellar luminosity will increase slightly. By analyzing the transit light curve it is possible to infer the physical properties of starspots, such as size, intensity, position and temperature. By detecting the same spot on consecutive transits, it is possible to obtain additional information such as the stellar rotation period in the planetary transit latitude, differential rotation, and magnetic activity cycles. Transit observations of CoRoT-18 and Kepler-17 were used to implement this model.

Análise wavelet da variabilidade do quasar 3C 273

Discovered in 1963, 3C 273 was the second quasar identified and cataloged in the Third Cambridge Catalog for radio sources, and the first one for which emission lines were identified with a hydrogen sequence redshifted. It is the brightest quasar of the celestial sphere, the most studied, analyzed, and with a resulting abundance of data available in a vast literature. The accurate analysis of the deviations of the spectral lines of quasars provides enough information to put in evidence the variation of fundamental constants of nature and similarly the universe expansion rate. The analysis of the variability of the light curves of these bodies, and the consequent accuracy of their periodicity, is of utmost importance as it provides an efficiency of their observations, enables a greater understanding of the physical phenomena, and makes it possible to conduct spectral observations on more accurate dates (when their light curves show pronounced peaks and therefore richer spectra information). In this master’s thesis twenty eight light curves from the quasar 3C 273 are studied, covering all the electromagnetic spectrum wavebands (radio emission to gamma rays), totaling in the analysis of four light curves for each waveband. We have applied the method of Continuous Wavelet Transform using the sixth-order (!0 = 6) Morlet wavelet function, and obtained excellent results in accordance with the literature.

Análise wavelet da variabilidade do quasar 3C 273

Discovered in 1963, 3C 273 was the second quasar identified and cataloged in the Third Cambridge Catalog for radio sources, and the first one for which emission lines were identified with a hydrogen sequence redshifted. It is the brightest quasar of the celestial sphere, the most studied, analyzed, and with a resulting abundance of data available in a vast literature. The accurate analysis of the deviations of the spectral lines of quasars provides enough information to put in evidence the variation of fundamental constants of nature and similarly the universe expansion rate. The analysis of the variability of the light curves of these bodies, and the consequent accuracy of their periodicity, is of utmost importance as it provides an efficiency of their observations, enables a greater understanding of the physical phenomena, and makes it possible to conduct spectral observations on more accurate dates (when their light curves show pronounced peaks and therefore richer spectra information). In this master’s thesis twenty eight light curves from the quasar 3C 273 are studied, covering all the electromagnetic spectrum wavebands (radio emission to gamma rays), totaling in the analysis of four light curves for each waveband. We have applied the method of Continuous Wavelet Transform using the sixth-order (!0 = 6) Morlet wavelet function, and obtained excellent results in accordance with the literature.

Análise wavelet em curvas de luz estelares de sistemas binários da missão espacial CoRoT

Binary systems are key environments to study the fundamental properties of stars. In this work, we analyze 99 binary systems identified by the CoRoT space mission. From the study of the phase diagrams of these systems, our sample is divided into three groups: those whose systems are characterized by the variability relative to the binary eclipses; those presenting strong modulations probably due to the presence of stellar spots on the surface of star; and those whose systems have variability associated with the expansion and contraction of the surface layers. For eclipsing binary stars, phase diagrams are used to estimate the classification in regard to their morphology, based on the study of equipotential surfaces. In this context, to determine the rotation period, and to identify the presence of active regions, and to investigate if the star exhibits or not differential rotation and study stellar pulsation, we apply the wavelet procedure. The wavelet transform has been used as a powerful tool in the treatment of a large number of problems in astrophysics. Through the wavelet transform, one can perform an analysis in time-frequency light curves rich in details that contribute significantly to the study of phenomena associated with the rotation, the magnetic activity and stellar pulsations. In this work, we apply Morlet wavelet (6th order), which offers high time and frequency resolution and obtain local (energy distribution of the signal) and global (time integration of local map) wavelet power spectra. Using the wavelet analysis, we identify thirteen systems with periodicities related to the rotational modulation, besides the beating pattern signature in the local wavelet map of five pulsating stars over the entire time span.

Análise wavelet em curvas de luz estelares de sistemas binários da missão espacial CoRoT

Binary systems are key environments to study the fundamental properties of stars. In this work, we analyze 99 binary systems identified by the CoRoT space mission. From the study of the phase diagrams of these systems, our sample is divided into three groups: those whose systems are characterized by the variability relative to the binary eclipses; those presenting strong modulations probably due to the presence of stellar spots on the surface of star; and those whose systems have variability associated with the expansion and contraction of the surface layers. For eclipsing binary stars, phase diagrams are used to estimate the classification in regard to their morphology, based on the study of equipotential surfaces. In this context, to determine the rotation period, and to identify the presence of active regions, and to investigate if the star exhibits or not differential rotation and study stellar pulsation, we apply the wavelet procedure. The wavelet transform has been used as a powerful tool in the treatment of a large number of problems in astrophysics. Through the wavelet transform, one can perform an analysis in time-frequency light curves rich in details that contribute significantly to the study of phenomena associated with the rotation, the magnetic activity and stellar pulsations. In this work, we apply Morlet wavelet (6th order), which offers high time and frequency resolution and obtain local (energy distribution of the signal) and global (time integration of local map) wavelet power spectra. Using the wavelet analysis, we identify thirteen systems with periodicities related to the rotational modulation, besides the beating pattern signature in the local wavelet map of five pulsating stars over the entire time span.

Contribuições para a análise de sinais neuronais e biomédicos

Following the new tendency of interdisciplinarity of modern science, a new field called neuroengineering has come to light in the last decades. After 2000, scientific journals and conferences all around the world have been created on this theme. The present work comprises three different subareas related to neuroengineering and electrical engineering: neural stimulation; theoretical and computational neuroscience; and neuronal signal processing; as well as biomedical engineering. The research can be divided in three parts: (i) A new method of neuronal photostimulation was developed based on the use of caged compounds. Using the inhibitory neurotransmitter GABA caged by a ruthenium complex it was possible to block neuronal population activity using a laser pulse. The obtained results were evaluated by Wavelet analysis and tested by non-parametric statistics. (ii) A mathematical method was created to identify neuronal assemblies. Neuronal assemblies were proposed as the basis of learning by Donald Hebb remain the most accepted theory for neuronal representation of external stimuli. Using the Marcenko-Pastur law of eigenvalue distribution it was possible to detect neuronal assemblies and to compute their activity with high temporal resolution. The application of the method in real electrophysiological data revealed that neurons from the neocortex and hippocampus can be part of the same assembly, and that neurons can participate in multiple assemblies. (iii) A new method of automatic classification of heart beats was developed, which does not rely on a data base for training and is not specialized in specific pathologies. The method is based on Wavelet decomposition and normality measures of random variables. Throughout, the results presented in the three fields of knowledge represent qualification in neural and biomedical engineering

Identificação não linear usando uma rede fuzzy wavelet neural network modificada

In last decades, neural networks have been established as a major tool for the identification of nonlinear systems. Among the various types of networks used in identification, one that can be highlighted is the wavelet neural network (WNN). This network combines the characteristics of wavelet multiresolution theory with learning ability and generalization of neural networks usually, providing more accurate models than those ones obtained by traditional networks. An extension of WNN networks is to combine the neuro-fuzzy ANFIS (Adaptive Network Based Fuzzy Inference System) structure with wavelets, leading to generate the Fuzzy Wavelet Neural Network - FWNN structure. This network is very similar to ANFIS networks, with the difference that traditional polynomials present in consequent of this network are replaced by WNN networks. This paper proposes the identification of nonlinear dynamical systems from a network FWNN modified. In the proposed structure, functions only wavelets are used in the consequent. Thus, it is possible to obtain a simplification of the structure, reducing the number of adjustable parameters of the network. To evaluate the performance of network FWNN with this modification, an analysis of network performance is made, verifying advantages, disadvantages and cost effectiveness when compared to other existing FWNN structures in literature. The evaluations are carried out via the identification of two simulated systems traditionally found in the literature and a real nonlinear system, consisting of a nonlinear multi section tank. Finally, the network is used to infer values of temperature and humidity inside of a neonatal incubator. The execution of such analyzes is based on various criteria, like: mean squared error, number of training epochs, number of adjustable parameters, the variation of the mean square error, among others. The results found show the generalization ability of the modified structure, despite the simplification performed

Localização de faltas em linhas de transmissão de múltiplos terminais a partir de registros oscilográficos sincronizados via transformada wavelet

The electric energy is essential to the development of modern society and its increasing demand in recent years, effect from population and economic growth, becomes the companies more interested in the quality and continuity of supply, factors regulated by ANEEL (Agência Nacional de Energia Elétrica). These factors must be attended when a permanent fault occurs in the system, where the defect location that caused the power interruption should be identified quickly, which is not a simple assignment because the current systems complexity. An example of this occurs in multiple terminals transmission lines, which interconnect existing circuits to feed the demand. These transmission lines have been adopted as a feasible solution to suply loads of magnitudes that do not justify economically the construction of new substations. This paper presents a fault location algorithm for multiple terminals transmission lines - two and three terminals. The location method is based on the use of voltage and current fundamental phasors, as well as the representation of the line through its series impedance. The wavelet transform is an effective mathematical tool in signals analysis with discontinuities and, therefore, is used to synchronize voltage and current data. The Fourier transform is another tool used in this work for extract voltage and current fundamental phasors. Tests to validate the location algorithm applicability used data from faulty signals simulated in ATP (Alternative Transients Program) as well as real data obtained from oscillographic recorders installed on CHESF s lines.

Estudo da transformada rápida wavelet e sua conexão com banco de filtros

In this work we presented an exhibition of the mathematical theory of orthogonal compact support wavelets in the context of multiresoluction analysis. These are particularly attractive wavelets because they lead to a stable and very efficient algorithm, that is Fast Transform Wavelet (FWT). One of our objectives is to develop efficient algorithms for calculating the coefficients wavelet (FWT) through the pyramid algorithm of Mallat and to discuss his connection with filters Banks. We also studied the concept of multiresoluction analysis, that is the context in that wavelets can be understood and built naturally, taking an important step in the change from the Mathematical universe (Continuous Domain) for the Universe of the representation (Discret Domain)

Estimação de potência em tempo real utilizando a transformada wavelet

The goal of the power monitoring in electrical power systems is to promote the reliablility as well as the quality of electrical power.Therefore, this dissertation proposes a new theory of power based on wavelet transform for real-time estimation of RMS voltages and currents, and some power amounts, such as active power, reactive power, apparent power, and power factor. The appropriate estimation the of RMS and power values is important for many applications, such as: design and analysis of power systems, compensation devices for improving power quality, and instruments for energy measuring. Simulation and experimental results obtained through the proposed MaximalOverlap Discrete Wavelet Transform-based method were compared with the IEEE Standard 1459-2010 and the commercial oscilloscope, respectively, presenting equivalent results. The proposed method presented good performance for compact mother wavelet, which is in accordance with real-time applications.