<p>This master's thesis explores whether time-frequency techniques can be utilized in a ground penetrating radar system. The system studied is the HUMUS system which has been developed at FOI, and which is used for the detection and classification of buried land mines. </p><p>The objective of this master's thesis is twofold. First of all it is supposed to give a theoretical introduction to the wavelet transform and wavelet packets, and also to introduce general time-frequency transformations. Secondly, the thesis presents and implements an adaptive method, which is used to perform the task of a feature extractor. </p><p>The wavelet theory presented in this thesis gives a first introduction to the concept of time-frequency transformations. The wavelet transform and wavelet packets are studied in detail. The most important goal of this introduction is to define the theoretical background needed for the second objective of the thesis. However, some additional concepts will also be introduced, since they were deemed necessary to include in an introduction to wavelets. </p><p>To illustrate the possibilities of wavelet techniques in the existing HUMUS system, one specific application has been chosen. The application chosen is feature extraction. The method for feature extraction described in this thesis uses wavelet packets to transform theoriginal radar signal into a form where the features of the signal are better revealed. One of the algorithms strengths is its ability to adapt itself to the kind of input radar signals expected. The algorithm will pick the "best" wavelet packet from a large number of possible wavelet packets.</p><p>The method we use in this thesis emanates from a previously publicized dissertation. The method proposed in that dissertation has been modified to the specific environment of the HUMUS system. It has also been implemented in MATLAB, and tested using data obtained by the HUMUS system. The results are promising; even"weak"objects can be revealed using the method.</p>

Safeguarding creative content in a digital form has become increasingly difficult. It is progressively easier to copy, modify and redistribute digital media, which causes great declines in business profits. For example, the International Federation of the Phonographic Industry estimates that in 2001 the worldwide sales of pirated music CDs were 475 million US dollars. While a large amount of time and money is committed to creating intellectual property, legal means have not proven to be sufficient for the protection of this property. Digital watermarking is a steganographic technique that has been proposed as a possible solution to this problem. A digital watermark hides embedded information about the origin, status, owner and/or destination of the data, often without the knowledge of the viewer or user. This dissertation examines a technique for digital watermarking which utilizes properties of the Discrete Wavelet Transform (DWT). Research has been done in this field, but which wavelet family is superior is not adequately addressed. This dissertation studies the influence of the wavelet family when using a blind, nonvisible watermark in digital media. The digital watermarking algorithm uses a database of multiple images with diverse properties. Various watermarks are embedded. Eight different families of wavelets with dissimilar properties are compared. How effective is each wavelet? To objectively measure the success of the algorithm, the influence of the mother wavelet, the imperceptibility of the embedded watermark and the readability of the extracted watermark, the Peak Signal-to-Noise Ratio and the Image Quality Index for each wavelet family and image are obtained. Two common categories of digital watermarking attacks are removing the watermark and rendering the watermark undetectable. To simulate and examine the effect of attacks on the images, noise is added to the image data. Also, to test the effect of reducing an image in size, each image containing the embedded watermark is compressed. The dissertation asks the questions: “Is the wavelet family chosen to implement the algorithm for a blind, nonvisible watermark in digital images of consequence? If so, which family is superior?” This dissertation conclusively shows that the Haar transform is the best for blind, non-visible digital watermarking.

In this thesis, a method to calculate scaling function coefficients for a new bi-orthogonal wavelet family derived directly from an impulse response waveform is presented. In literature, the Daubechies wavelets (DB wavelet) and the Morlet wavelet are the most commonly used wavelets for the dyadic wavelet transform (DWT) and the continuous wavelet transform (CWT), respectively. For a specific vibration signal processing application, a wavelet basis that is similar or is derived directly from the signal being studied proves to be superior to the commonly used wavelet basis. To assure a wavelet basis has a direct relationship to the signal being studied, a new formula is proposed to calculate coefficients which capture the characteristics of an impulse response waveform. The calculated coefficients are then used to develop a new bi-orthogonal wavelet family.

El avance de las tecnologías de los microprocesadores y ordenadores ha permitido sustituir las protecciones electromecánicas y analógicas clásicas por protecciones digitales. Sin embargo, los algoritmos empleados en éstas últimas tienen serias dificultades cuando las señales procedentes de los transductores de las corrientes y tensiones están afectadas por la saturación de los mismos o por efectos de ferrorresonancia respectivamente, o cuando la falta que se presenta en la línea está afectada por un arco dinámico.Por otro lado, en los últimos años se habían hecho pequeños avances en la aplicación de la inteligencia artificial y en especial en redes neuronales a los sistemas de energía eléctrica. Éstas resultaban especialmente útiles en la predicción del flujo de carga y en la clasificación de patrones de faltas. El término clasificación de patrones engloba un amplio marco de problemas de procesado de información de gran importancia práctica. Con frecuencia estos problemas se resuelven mediante técnicas estadísticas, desarrollando un algoritmo capaz de clasificar un correctamente un patrón no visto anteriormente. Una aproximación al reconocimiento estadístico de patrones se realiza mediante el teorema de Bayes, que expresa la probabilidad de que un patrón pertenezca a una determinada clase, expresando ésta probabilidad a posteriori en función de medidas realizadas previamente. En función de las características observadas se divide el espacio en regiones de decisión separadas por fronteras de decisión o clasificación. Análogamente, las salidas de una red neuronal se pueden interpretar como las probabilidades obtenidas a partir de la función de error (minimizar la función error durante el entrenamiento de la red neuronal es equivalente a buscar la máxima probabilidad), y la red neuronal aproxima las fronteras del clasificador Bayesiano óptimo.Ante estos hechos, y la gran ventaja que supone el modo de trabajo en paralelo de las redes neuronales, nos propusimos como objetivo buscar nuevos caminos en el campo de las protecciones de las redes eléctricas por medio del estudio de las redes neuronales de sistemas de protección que resuelvan los problemas anteriormente apuntados.La metodología empleada consistió en el entrenamiento de los diferentes tipos de redes neuronales utilizadas en los relés de protección mediante datos generados, para distintos tipos de fallos, con un programa de transitorios electromagnéticos (EMTDC/PSCAD) aplicado a un modelo de red muy general que incluye todas las posibles topologías y niveles de carga. Estos patrones fueron empleados para entrenar las redes neuronales mediante un programa en C++ realizado por el autor.También se incorporó en este trabajo, el estudio y la aplicación de la transformada wavelet, que presenta una serie de ventajas frente a métodos tradicionales de procesado de señales. Entre las herramientas tradicionales de análisis de sistemas eléctricos de potencia, se encuentran numerosos algoritmos, basados entre otros, en la transformada de Fourier, filtros de Kalman, etc. Sin embargo, si ocurre un transitorio, las formas de onda asociadas son no periódicas, conteniendo oscilaciones de alta y de baja frecuencia superpuestas a la frecuencia de funcionamiento del sistema eléctrico. En tal situación, debido a que la transformada de Fourier realiza un promedio de la contribución de las frecuencias se pierde la localización de la perturbación en el tiempo. El análisis mediante wavelets supera ésta limitación, realizando un procesado de la señal, que proporciona información en tiempo y en frecuencia. Por ello, la transformada wavelet es una potente ayuda para el análisis, estudio e interpretación de los distintos fenómenos transitorios que se pueden presentar en un sistema eléctrico de potencia. Además, en este trabajo se ha implementado la transformada wavelet mediante una red neu-ronal, lo que nos permite integrar dentro de la red neuronal general de reconocimiento de pa-trones, una subred encargada de llevar a cabo el procesado de señal. El funcionamiento en paralelo de la red neuronal con la información suministrada por las wavelets ha permitido incrementar la velocidad y seguridad de la respuesta del relé neuronal en los primeros instan-tes del fallo. Asimismo, uno de los objetivos de este trabajo era realizar la implementación práctica del diseño realizado en un sistema electrónico que permitiera comprobar la eficacia del mismo. Para llevar a cabo el montaje experimental se necesitaba un sistema que permitiera simular los sistemas eléctricos similares a los empleados en el proceso de diseño y entrenamiento del relé. El Departamento de Ingeniería Eléctrica de la Universidad de Bath cuenta con el equipo RTDS, que constituye el complemento del sistema de simulación PSCAD, con el que es posi-ble llevar a cabo la simulación y ensayo de prototipos de equipos eléctricos. Bajo la dirección del Prof. Aggarwal se llevó a cabo las pruebas de laboratorio del relé neuronal que resultaron plenamente satisfactorias. Los alentadores resultados obtenidos son un buen estímulo para el uso de las redes neuronales en las protecciones de alta velocidad para líneas de transmisión de alta tensión ya que hemos obtenido un tiempo de respuesta en la detección en la red neuronal de incluso 1.8 ms para fallos cercanos al relé. El relé también ha dado una buena respuesta frente a ruidos, pérdida de información y cambios bruscos de carga. / The great advance of the microprocessor and computer technology has allowed the electromechanical and analog protection devices to be substituted by digital ones. However, the algorithms used in digital protections have some disadvantages related to the errors caused by current transformer saturation, voltage transformer ferro-resonance or by dynamics arcing faults. Over the past 10 years there have been some advances in the application of artificial intelligence, especially of neural networks, on power system analysis. These applications were useful in the prediction of optimum load flow and fault pattern classification. The term pattern classification encompasses a wide range of information processing problems of great practical significance. Often the framework in which to formulate solutions to pattern recognition is the statistical one, with the develop of an algorithm to be able to correctly classify a previously unseen pattern. One approach to statistical pattern recognition is using Bayes´ theorem, which gives the probability of the pattern belonging to a particular class, and expresses this posterior probability in terms of previous measurements. The space is divided up into decision regions depending on the observed features. The boundaries between regions are known as decision boundaries. The outputs of a neural network can be interpreted as posterior probabilities calculated with the error function (the network training is based on maximum likelihood which is equivalent to minimization of an error function), and the neural network approximates the decision boundaries of the Bayes´ theorem.For these reasons and because of the advantage of the parallel processing capabilities of the neural networks, our objective here is to search for new applications of neural networks on power system protection in order to improve it and solve the problems mentioned above.In order to do this in this thesis, the artificial neural networks are applied to the protection of high voltage transmission lines, assuming dynamic arcing faults, the current transformer saturation, the change of the short circuit levels, the change of the power network topology, the bad and noisy data, and sudden load changes.The methodology carried out in a special training process of the neural networks, using protection relays by means of simulated faults data, obtained by the electromagnetic transient program (EMTDC/PSCAD) applied to a generalized power network model which includes all the possible topologies and load levels. The training algorithm was implemented by the author in the C++ language program.Within this project we included the study and application of the wavelet transform, which showed a series of advantages in front of traditional methods in signal processing. In traditional power signal analysis tools, among several algorithms, the Fourier transform has been used as well as the Kalman filtering, etc. However, in presence of non stationary signals the performance of these techniques are limited. Thus, if there is a local transient over some small interval of time in the lifetime of the signal, the transient will contribute to the Fourier transform, but its location on the time axis will be lost. Wavelets analysis overcomes this limitation by employing an analyzing function that is local both in time and frequency. The wavelet transform is a powerful tool for the study and analysis of transient phenomena in electric power systems.Furthermore, in this work the wavelet transform has been implemented with a neural network which allows us to incorporate it within the whole network for pattern recognition. Both neural networks along with the information supplied by the wavelets, have made it possible to increase the speed and reliability of the relay, especially during the fault inception.Also, one of our aims was to carry out the practical implementation of an electronic board in order to test the performance of the neural relay. To do this, it was necessary to use equipment to carry out the laboratory test, by emulating the same or a similar system employed while designing and training the relay.Prof. R. K. Aggarwal, in the Electrical department in the University of Bath expertise in the application of signal processing and Artificial Intelligence technology for the development of novel intelligent relays for Power Systems, both for transmission and distribution systems. Their experience is not only in the CAD work but also in the design and engineering of proto-type hardware. To do this the RTDS (Real Time Digital Simulator) system was employed. The obtained results were fully satisfactory.These successful tests results encourage investment in neural networks in high speed protec-tion for high voltage transmission lines. The response time is even less than 1.8 ms for faults close to the relay, which has a good performance in front of noise, faulty data and sudden change of load.

In typical statistical parametric mapping (SPM) of fMRI data, the functional data are pre-smoothed using a Gaussian kernel to reduce noise at the cost of losing spatial specificity. Wavelet approaches have been incorporated in such analysis by enabling an efficient representation of the underlying brain activity through spatial transformation of the original, un-smoothed data; a successful framework is the wavelet-based statistical parametric mapping (WSPM) which enables integrated wavelet processing and spatial statistical testing. However, in using the conventional wavelets, the functional data are considered to lie on a regular Euclidean space, which is far from reality, since the underlying signal lies within the complex, non rectangular domain of the cerebral cortex. Thus, using wavelets that function on more complex domains such as a graph holds promise. The aim of the current project has been to integrate a recently developed spectral graph wavelet transform as an advanced transformation for fMRI brain data into the WSPM framework. We introduce the design of suitable weighted and un-weighted graphs which are defined based on the convoluted structure of the cerebral cortex. An optimal design of spatially localized spectral graph wavelet frames suitable for the designed large scale graphs is introduced. We have evaluated the proposed graph approach for fMRI analysis on both simulated as well as real data. The results show a superior performance in detecting fine structured, spatially localized activation maps compared to the use of conventional wavelets, as well as normal SPM. The approach is implemented in an SPM compatible manner, and is included as an extension to the WSPM toolbox for SPM.

This master's thesis explores whether time-frequency techniques can be utilized in a ground penetrating radar system. The system studied is the HUMUS system which has been developed at FOI, and which is used for the detection and classification of buried land mines. The objective of this master's thesis is twofold. First of all it is supposed to give a theoretical introduction to the wavelet transform and wavelet packets, and also to introduce general time-frequency transformations. Secondly, the thesis presents and implements an adaptive method, which is used to perform the task of a feature extractor. The wavelet theory presented in this thesis gives a first introduction to the concept of time-frequency transformations. The wavelet transform and wavelet packets are studied in detail. The most important goal of this introduction is to define the theoretical background needed for the second objective of the thesis. However, some additional concepts will also be introduced, since they were deemed necessary to include in an introduction to wavelets. To illustrate the possibilities of wavelet techniques in the existing HUMUS system, one specific application has been chosen. The application chosen is feature extraction. The method for feature extraction described in this thesis uses wavelet packets to transform theoriginal radar signal into a form where the features of the signal are better revealed. One of the algorithms strengths is its ability to adapt itself to the kind of input radar signals expected. The algorithm will pick the "best" wavelet packet from a large number of possible wavelet packets. The method we use in this thesis emanates from a previously publicized dissertation. The method proposed in that dissertation has been modified to the specific environment of the HUMUS system. It has also been implemented in MATLAB, and tested using data obtained by the HUMUS system. The results are promising; even"weak"objects can be revealed using the method.

This thesis studies the application of the wavelet filter bank (WFB) in perceptual audio coding by providing brief overviews of perceptual coding, psychoacoustics, wavelet theory, and existing wavelet coding algorithms. Furthermore, it describes the poor frequency localization property of the WFB and explores one filter design method, in particular, for improving channel separation between the wavelet bands. A wavelet audio coder has also been developed by the author to test the new filters. Preliminary tests indicate that the new filters provide some improvement over other wavelet filters when coding audio signals that are stationary-like and contain only a few harmonic components, and similar results for other types of audio signals that contain many spectral and temporal components. It has been found that the WFB provides a flexible decomposition scheme through the choice of the tree structure and basis filter, but at the cost of poor localization properties. This flexibility can be a benefit in the context of audio coding but the poor localization properties represent a drawback. Determining ways to fully utilize this flexibility, while minimizing the effects of poor time-frequency localization, is an area that is still very much open for research.

Safeguarding creative content in a digital form has become increasingly difficult. It is progressively easier to copy, modify and redistribute digital media, which causes great declines in business profits. For example, the International Federation of the Phonographic Industry estimates that in 2001 the worldwide sales of pirated music CDs were 475 million US dollars. While a large amount of time and money is committed to creating intellectual property, legal means have not proven to be sufficient for the protection of this property. Digital watermarking is a steganographic technique that has been proposed as a possible solution to this problem. A digital watermark hides embedded information about the origin, status, owner and/or destination of the data, often without the knowledge of the viewer or user. This dissertation examines a technique for digital watermarking which utilizes properties of the Discrete Wavelet Transform (DWT). Research has been done in this field, but which wavelet family is superior is not adequately addressed. This dissertation studies the influence of the wavelet family when using a blind, nonvisible watermark in digital media. The digital watermarking algorithm uses a database of multiple images with diverse properties. Various watermarks are embedded. Eight different families of wavelets with dissimilar properties are compared. How effective is each wavelet? To objectively measure the success of the algorithm, the influence of the mother wavelet, the imperceptibility of the embedded watermark and the readability of the extracted watermark, the Peak Signal-to-Noise Ratio and the Image Quality Index for each wavelet family and image are obtained. Two common categories of digital watermarking attacks are removing the watermark and rendering the watermark undetectable. To simulate and examine the effect of attacks on the images, noise is added to the image data. Also, to test the effect of reducing an image in size, each image containing the embedded watermark is compressed. The dissertation asks the questions: “Is the wavelet family chosen to implement the algorithm for a blind, nonvisible watermark in digital images of consequence? If so, which family is superior?” This dissertation conclusively shows that the Haar transform is the best for blind, non-visible digital watermarking.

O presente trabalho apresenta uma comparação de duas técnicas para a análise tempo - frequência em análise de qualidade de energia elétrica para sinais de tensão que contenham distúrbios individuais ou simultâneos. Dessa forma, o objetivo, desta dissertação, é encontrar uma ferramenta que forneça as características e parâmetros para a localização, identificação e classificação de tais distúrbios. O estudo consiste na análise do desempenho da Transformada Wavelet Discreta e da Transformada-S, principalmente, quando os sinais são analisados na presença de múltiplos distúrbios. Ambas as transformadas fornecem informação importante nos domínios do tempo e da frequência. No entanto, essas ferramentas não tem sido amplamente exploradas para análise de múltiplos distúrbios. Neste contexto, ambas as transformadas são testadas para conhecer seus desempenhos e suas capacidades de identificação e localização de eventos de qualidade de energia elétrica. Para finalizar, é projetado um sistema classificador baseado em arvore de decisão capaz de reconhecer quinze tipos de distúrbios diferentes. / This work presents a comparison of two methods for time-frequency analysis applied in Power Quality signals containing single or multiple disturbances. In this way, the aim of this work is to apply tools that supply the parameters and characteristics to identify, locate and classify Power Quality disturbances. For that, the proposed method analyzes the performance of the Wavelet and S transforms, mainly when the signals are with more than one disturbance type. Both mathematical tools supply important information on the time and frequency domain. However, these tools have not been thoroughly used to analyze multiple events locate Power Quality events. In this contest, both transforms are tested in order to assess their performance to identify and locate electrical power quality events. According to a decision tree classifier, fifteen types of single and combined power disturbances are well recognized.

[pt] Essa dissertação apresenta um codificador de imagens para baixas taxas de bits utilizando a decomposição da imagem em 10 sub-bandas através da aplicação da transformada wavelet. Uma técnica de redução de irrelevância visual é usada para descartar blocos de coeficientes das sub-bandas de alta freqüência (2 a 10). Os blocos remanescentes são classificados em bordas e não bordas e codificados através da técnica ECTCVQ ( Entropy-Constrained Trellis Coded Vector Quantization). Já a primeira sub-banda é codificada através da técnica PTCQ( Predictive Trellis Coded Quantization) com preservação de bordas. Na alocação de bits entre as sub-bandas é utilizado o algoritmo de Wersterink et al. Os resultados obtidos mostram um desempenho muito superior ao padrão JPEG, e bons resultados quando comparados a técnica de codificação de imagens recentes. / [en] This dissertation presentes a low bit rate image coder using a 10 sub-band image decomposition base don the wavelet transform. Some blocks of coefficients of the high frequency sub-bands are discarded by a technique of irrelevancy reduction. The remaning blocks are classified into edges and non-edges, and coded by ECTCVQ (Entropy- constrained Trellis Vector Quantization). The fist sub- band is coded by an edge preserving PTCQ (Predictive Trellis Coded Quantization), also proposed in this work. The Westerink et al. algorithm is used to allocate the bits between the sub-bands. The results obtained show that the performance of the proposed coder is Significantly superior so the one obtained with the standard JPEG. Moreover, good results are achivied as compared to recently proposed techniques of images coding.