Time-frequency analysis is a powerful tool for signal analysis and processing. The Fourier transform and wavelet transforms are used extensively as is the Short-Time Fourier Transform (or Gabor transform). In 1996 the Stockwell transform was introduced to maintain the phase of the Fourier transform, while also providing the progressive resolution of the wavelet transform. The discrete orthonormal Stockwell transform is a more efficient, less redundant transform with the same properties. There has been little work on mathematical properties of the Stockwell transform, particularly how it behaves under operations such as translation and modulation. Previous results do discuss a resolution of the identity, as well as some of the function spaces that may be associated with it [2]. We extend the resolution of the identity results, and behaviour under translation, modulation, convolution and differentiation. boundedness and continuity properties are also developed, but the function spaces associated with the transform are unrelated to the focus of this thesis. There has been some work on image processing using the Stockwell transform and discrete orthonormal Stockwell transform. The tests were quite preliminary. In this thesis, we explore some of the mathematics of the Stockwell transform, examining properties, and applying it to various continuous examples. The discrete orthonormal Stockwell transform is compared directly with Newland’s harmonic wavelet transform, and we extend the definition to include varitions, as well as develop the discrete cosine based Stockwell transform. All of these discrete transforms are tested against current methods for image compression.

This master’s thesis deals with issues of the detection of K-complexes in EEG sleep signals. Record from an electroencephalograph is important for non-invasive diagnosis and research of brain activity. The scanned signal is used to examine sleep phases, disturbances, states of consciousness and the effects of various substances. This work follows the automatic detection of K-complexes, because the manual labeling of graphoelements is complicated. Two approaches were used –Stockwell transform and bandpass filtration followed by TKEO operator application. All algorithms were created in the MATLAB R2014a.

Ce travail a pour objectif de caractériser et analyser le bruit de frottement des étoffes textiles généré lors de l’activité d’un individu (marche et course). Le présent travail apporte une contribution pour la caractérisation physique du bruit de frottement grâce à des paramètres physiques du son (bruit) et grâce à une nouvelle méthode de traitement du signal sonore des étoffes textiles, la transformée en S (transformée de Stokwell). L’évaluation sensorielle du bruit a été menée grâce à des panélistes entraînés en appliquant la méthode d’Analyse Descriptive Quantitative. Dans ce cadre, l’influence de l’armure d’étoffes en coton écru sur les propriétés sonores a été analysée. La corrélation entre les paramètres mécaniques des tissus qui décrivent l’état de surface et la compression de l’étoffe (mesurés par la chaîne de mesure Kawabata Evaluation System) et le niveau sonore global du bruit de frottement a été effectuée. Une corrélation entre le niveau sonore et les descripteurs sensoriels a été également menée. Le bruit d’une veste d’homme, confectionnée en deux types de prototypes présentant des variantes de manches, a été analysé en situation réelle, dans une chambre anéchoïque.Selon le traitement des signaux sonores, l’armure sergé 3 est la plus bruyante avec un niveau sonore, une amplitude du maximum les plus importants, pour les deux vitesse de frottement (marche et course), et une fréquence de maximum se trouvant dans la zone fréquentielle pour laquelle l’oreille humaine est la plus sensible. L’armure satin 4 est la plus ‘furtive’ avec un niveau sonore, une amplitude du maximum la moins importante et une fréquence correspondant importante et moins perceptible. Les résultats obtenus par l'analyse sensorielle sont cohérents avec les résultats obtenus en terme instrumental. Les panélistes qui participent à l'évaluation du bruit de frottement des étoffes textile ont perçu le bruit du satin 4 comme le bruit le plus sourd et le plus homogène, alors que le bruit du sergé 3 a été perçu comme le bruit le plus énergique et le plus disharmonique. Les modèles établis expriment que le niveau sonore augmente en fonction de la rugosité de surface et diminue en fonction de la résilience et de l'énergie de compression. Ainsi, plus que le niveau sonore est important, plus que le bruit est perçu plus polyphonique et plus grattant. Les bruits générés par le frottement de la veste avec les deux types de manche sont similaires en termes instrumental et sensoriel. / This work aims to characterize and analyze the frictional noise of textile materials generated during the activity of a subject (walking and running). This work contributes to the physical characterization of frictional noise characterized by physical parameters of sound (noise) and thanks to a new method of treatment of the acoustic signal, Stokwell-transform. Sensory evaluation of frictional noise was conducted by trained panelists using the Quantitative Descriptive Analysis method. In this context, the influence of the weave patterns of raw cotton fabrics on sound properties was analyzed. Correlations between the mechanical parameters of the fabric which describe the surface and the compressional proprieties of fabrics (measured by the Kawabata Evaluation System) and the sound level of the frictional noise were conducted. Correlations between the noise level and sensory descriptors were also conducted. The sounds of a man's jacket, fabricated in two types of prototypes with sleeves variants were analyzed in situation case, in an anechoic room. According to the treatment of acoustic signal, the twill 3 weave pattern is the noisiest one with a most important level sound and highest amplitude for the two types of movement (walking and running). The satin 4 weave pattern, which is the less noisy, presents a sound level and its highest amplitude is the less important. The frequency of highest amplitude is less important for twill 3 than satin 4. The results obtained by sensory analysis are coherent with the results obtained by instrumental characterization. The subjects participating to sensory evaluation of frictional noise of these fabrics perceived that the noise of satin 4 as the most muffled and most homogeneous noise, while the noise of twill 3 was perceived as the most dynamic and the most disharmonic one. Proposed models express that the sound level increases with the surface roughness and decreases with the resilience and the compression energy. The more sound level is important, the more the noise is perceived as polyphonic and scratching. The noise generated by the friction of the jacket with the two types of sleeves is similar whatever the evaluation.

Fundação de Amparo a Pesquisa no Estado do Rio Grande do Sul / Electricity consumption in homes and workplaces has been growing steadily over the decades and attitudes to reduce these costs should be taken. An interesting solution is to provide to electricity users, and also to the energy company, detailed data of individual consumption of each electrical appliance. To accomplish this, researchers in the field have focused their efforts on non-intrusive methods of load identification, where a single energy meter is able to desagreggate the appliances by monitoring the total consumption of electricity of that location. Non-intrusive methods are easy to install and demand little maintenance, but require a robust method for identifying these loads. Therefore, the aim of this work is to investigate nonintrusive methods of recognition of electrical appliances to find the desaggregated consumption of these loads. Among these methods, there are the already widely used image recognition pattern methods, that now are been used also to detect electrical devices. In this paper, two of these techniques are discussed, the Principal Component Analisys, a classical method in the literature, and the Vector Projection Length, a completely new method and never used in the loads recognition field before. Current and voltage data were collected from 16 residential appliances, involving all types of loads (resistive, inductive, electronic and hybrid/other types). These data were used as training samples and test samples (unknown samples). A study is carried out using the current and also the power, independently, as load signatures. Also, a comparative analysis of the results of signatures in the time domain and time-frequency (Stowkwell transform) is conducted. As the main contributions to this work, we verified that the Vector Projection Length for load identification is quite feasible, with results up to 96% of tested appliances being identified. However, the results with Principal Component Analisys did not presented the same performance, reaching only 81% of accuracy rate. Comparing the signatures, it became clear that one should use the current in the time-frequency domain for better performance. Neither the use of power, or the time domain obtained satisfactory results of load identification when applying image pattern recognition techniques to load recognition. / O consumo de eletricidade em residências e ambientes de trabalho vem crescendo continuamente ao longo das décadas e atitudes para reduzir estes gastos devem ser tomadas. Uma solução interessante é fornecer aos usuários de energia elétrica, e também à própria concessionária, dados detalhados de consumo individual de cada equipamento elétrico. Para alcançar este objetivo, pesquisadores na área tem focado seus esforços em métodos não-intrusivos de identificação das cargas (equipamentos elétricos), onde um único medidor de energia é capaz de desagregar os equipamentos através do monitoramento do consumo total de energia elétrica daquele local. Métodos não-intrusivos são de fácil instalação e de pouca manutenção, porém requerem um robusto método de identificação destas cargas. Portanto, o objetivo deste trabalho é investigar métodos não-intrusivos de reconhecimento de equipamentos elétricos para encontrar o consumo desagregado destas cargas. Dentre estes métodos, existem os já muito utilizados no reconhecimento de padrões em imagens, mas que agora tem sido também usados para detectar cargas elétricas. Neste trabalho duas destas técnicas são abordadas, a Principal Component Analisys, método clássico na literatura, e o Vector Projection Length, um método completamente novo e nunca usado no reconhecimento de cargas. Coletou-se dados de corrente e tensão de 16 equipamentos elétricos residenciais dos mais variados tipos, envolvendo todos os tipos de cargas existentes (resistivas, indutivas, eletrônicas e híbridas/outros tipos). Estes dados coletados foram utilizados como amostras de treinamento e amostras de teste (amostras desconhecidas). Como assinatura das cargas é realizado um estudo empregando corrente e também potência, de forma independente. Ainda, uma análise comparativa de resultados das assinaturas no domínio do tempo e do tempo-frequência (Transformada de Stowkwell) é conduzido. Como principais contribuições para este trabalho obteve-se que o uso do Vector Projection Length na identificação de equipamentos é bastante viável, com resultados de até 96% dos equipamentos testados sendo identificados. Já os resultados com o Principal Component Analisys ficaram abaixo de seu concorrente, atingindo 81% de taxa de acertos. Comparando as assinaturas, ficou claro que deve-se utilizar a corrente no domínio do tempo-frequência para uma melhor performance. Nem o uso da potência, nem o domínio do tempo obtiveram resultados satisfatórios de identificação quando empregados.

FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / This paper presents an automatic fault location method in transmission lines based on the Travelling Waves Theory (TWT) using the Stockwell Transform (ST) to determine the travelling waves propagation time and the dominant frequency of transient signals generated by faults. The method considers the case where there is no communication between terminals or loss of synchronism between the devices responsible for estimating the location of faults using, therefore, only data from one terminal. Single-phase faults only involving one of the phases and the earth area evaluated, which occur in the first half of a transmission line of unknown parameters. It is observed that the method (i) wasnât sensitive to fault resistance variations and inception angle and (ii) the obtained results presented errors between 0,10% and 5,82% for faults that occurred between 7km and 99km from the monitoring terminal. To improve the accuracy of estimating the fault location, an Artificial Neural Network (ANN) of the type MLP (Multi-Layer Perceptron) is designed, and trained with characteristics extracted from the faulty signals using ST. The ATP (Alternative Transient Program) software was adopted for simulation of a three phase transmission line which voltage signals were sampled at 200kHz. The simulations were performed exploring 1280 combinations of the following parameters: fault locations, fault resistances and inception angle. The method was developed using the software MATLABÂ. According to the obtained results, the combination of ST with ANN presented better results than the application of ST and TWT. Such improvement is highlighted for the estimation of fault location at greater distances from the monitoring terminal, with errors between 0,02% and 1,56% for faults that occurred between 7km and 99km from the monitoring terminal. / Este trabalho apresenta um mÃtodo automÃtico de localizaÃÃo de faltas em linhas de transmissÃo baseado na Teoria das Ondas Viajantes (TOV) utilizando a Transformada de Stockwell (TS) para determinaÃÃo dos tempos de propagaÃÃo das ondas viajantes e da frequÃncia dominante dos sinais transitÃrios gerados pelas situaÃÃes de falta. O mÃtodo considera o caso em que nÃo hà comunicaÃÃo entre terminais ou hà perda de sincronismo entre os equipamentos responsÃveis pela estimaÃÃo da localizaÃÃo das faltas utilizando, portanto, dados provenientes de apenas um terminal. Consideram-se faltas monofÃsicas envolvendo uma das fases e a terra, as quais ocorrem na primeira metade de uma linha de transmissÃo de parÃmetros desconhecidos. Observa-se que o mÃtodo (i) nÃo se mostrou sensÃvel a variaÃÃes de resistÃncia de falta e Ãngulo de incidÃncia e (ii) os resultados obtidos apresentam erros entre 0,10% e 5,82% para faltas que ocorreram entre 7km e 99km do terminal de monitoramento. Para a melhoria da precisÃo na estimaÃÃo da localizaÃÃo das faltas foi projetada uma Rede Neural Artificial (RNA) do tipo MLP (Multi-Layer Perceptron), treinada a partir de caracterÃsticas dos sinais faltosos extraÃdas atravÃs da TS. Foram utilizados os sinais trifÃsicos de tensÃo amostrados na frequÃncia de 200kHz gerados a partir de simulaÃÃes no software ATP (Alternative Transiente Program), no qual foram realizadas 1280 simulaÃÃes explorando diversas localizaÃÃes e resistÃncias de falta e Ãngulo de incidÃncia. O mÃtodo foi aplicado utilizando o software MATLABÂ. De acordo com os resultados obtidos, a combinaÃÃo da TS e RNA projetada apresentou melhores resultados do que a aplicaÃÃo da TS e TOV, destacando-se na estimaÃÃo da localizaÃÃo de faltas que ocorreram a maiores distÃncias do terminal de monitoramento, com erros entre 0,02% e 1,56% para faltas que ocorreram entre 7km e 99km do terminal de monitoramento.

This thesis deals with the detection of QRS complexes from electrocardiograms using time-frequency analysis. Detection procedures are based on wavelet and Stockwell transform. The theoretical part describes the basics of electrocardiography, then introduces common approaches to time-frequency analysis, such as short-time Fourier transform (STFT), wavelet transform and Stockwell transform. These algorithms were tested on a set of electrograms from the MIT-BIH and CSE-MO1 arrhythmia database. For the CSE database worked best the method based on the wavelet transform with the filter bank Symlet4, with the resulting value of sensitivity 100 % and positive predictivity 99.86%. For the MIT database had the best performance the detector using the Stockwell transform with values of sensitivity 99.54% and positive predictivity 99.68%. The results were compared with the values of other authors mentioned in the text.