This study proposes a new spectral representation called the Zeros of Z-Transform (ZZT), which is an all-zero representation of the z-transform of the signal. In addition, new chirp group delay processing techniques are developed for analysis of resonances of a signal. The combination of the ZZT representation with the chirp group delay processing algorithms provides a useful domain to study resonance characteristics of source and filter components of speech. Using the two representations, effective algorithms are developed for: source-tract decomposition of speech, glottal flow parameter estimation, formant tracking and feature extraction for speech recognition. The ZZT representation is mainly important for theoretical studies. Studying the ZZT of a signal is essential to be able to develop effective chirp group delay processing methods. Therefore, first the ZZT representation of the source-filter model of speech is studied for providing a theoretical background. We confirm through ZZT representation that anti-causality of the glottal flow signal introduces mixed-phase characteristics in speech signals. The ZZT of windowed speech signals is also studied since windowing cannot be avoided in practical signal processing algorithms and the effect of windowing on ZZT representation is drastic. We show that separate patterns exist in ZZT representations of windowed speech signals for the glottal flow and the vocal tract contributions. A decomposition method for source-tract separation is developed based on these patterns in ZZT. We define chirp group delay as group delay calculated on a circle other than the unit circle in z-plane. The need to compute group delay on a circle other than the unit circle comes from the fact that group delay spectra are often very noisy and cannot be easily processed for formant tracking purposes (the reasons are explained through ZZT representation). In this thesis, we propose methods to avoid such problems by modifying the ZZT of a signal and further computing the chirp group delay spectrum. New algorithms based on processing of the chirp group delay spectrum are developed for formant tracking and feature estimation for speech recognition. The proposed algorithms are compared to state-of-the-art techniques. Equivalent or higher efficiency is obtained for all proposed algorithms. The theoretical parts of the thesis further discuss a mixed-phase model for speech and phase processing problems in detail.

A Constant Proportion Debt Obligation is a credit derivative which has been introduced to generate a surplus return over a riskless market return. The surplus payments should be obtained by synthetically investing in a risky asset (such as a credit index) and using a linear leverage strategy which is capped for bounding the risk. In this thesis, we investigate two approaches for investigation of constant proportion debt obligations. First, we search for an optimal leverage strategy which minimises the mean-square distance between the final payment and the final wealth of constant proportion debt obligation by the use of optimal control methods. We show that the optimal leverage function for constant proportion debt obligations in a mean-square sense coincides with the one used in practice for geometric type diffusion processes. However, the optimal strategy will lead to a shortfall for some cases. The second approach of this thesis is to develop a pricing formula for constant proportion debt obligations. To do so, we consider both the early defaults and the default on the final payoff features of constant proportion debt obligations. We observe that a constant proportion debt obligation can be modelled as a barrier option with rebate. In this respect, given the knowledge on barrier options, the pricing equation is derived for a particular leverage strategy.

This thesis explores one possible method of preventing helicopter crashes caused by brownout using the noise generated by the helicopter rotor as an altimeter. The hypothesis under consideration is that the helicopter's height, velocity, and obstacle locations with respect to the helicopter, can be determined by comparing incident and reflected rotor noise signals, provided adequate bandwidth and signal to noise ratio. Heights can be determined by measuring the cepstrum of the reflected helicopter noise. The velocity can be determined by measuring small amounts of Doppler distortion using the Mellin-Scale Transform. Height and velocity detection algorithms are developed, optimized for this application, and tested using a microphone array. The algorithms and array are tested using a hemianechoic chamber and outside in Georgia Tech's Burger Bowl. Height and obstacle detection are determined to be feasible with the existing array. Velocity detection and surface mapping are not successfully accomplished.

This Master degree paper analyses hyperbolic image filtering in spaces of different dimensionality. It investigates the problem of optimal filtering space selection. Several popular image compression methods (both lossless and lossy) are reviewed. This paper analyses the problems of image smoothness parameter discovering, image dimensionality changing, hyperbolic image filtering and filtering efficiency evaluation and provides the solution methods of the problems. Schemes for the experimental examination of theoretical propositions and hypotheses are prepared. This paper comprehensively describes experiments with one-, two- and threedimensional images and the results of the experiments. Conclusions about the efficiency of hyperbolic image filtering in other than "native" image space are based on the results of the experiments. The criterion for the selection of optimal image filtering space is evaluated. Guidelines for further research are also discussed. The presentation Specific Features of Hyperbolic Image Filtering, which was based on this Master degree paper, was made at the conference Mathematics and Mathematical Modeling (KTU – 2004). This text is available in appendixes.

Sakykime, kad F yra normuota parabolinė tikrinė forma pilnosios modulinės grupės atžvilgiu, L(s, F) yra susieta su L funkcijos sąsūka L(s, F, χ) su Dirichlė charakteriu moduliu q, kai q yra pirminis skaičius. Bakalauro darbe įrodyta ribinė teorema L funkcijų sąsūkų argumentui arg L(s, F, χ). / Let F(z) a holomorfic normalized Hecke eigen cups form of weight κ for the full modular group, L(s, F), s = σ + it, be the L-function attached to the form F. Let L(s, F, χ) denote a twist of L(s, F) with a Dirichlet character χ modulo q, by the Dirichlet series and can be analytically continued to an entire function. It has an Euler product over prime numbers. We obtain the weak dinvergence for probability measures μQ(arg L(s, F, χ) ∈ A), A ∈ B(γ), where γ is the unit circle on the complex plane, as Q → ∞. For the proof, the method of characteristic transforms and the limit measures in limit theorems obtained are defined characteristic transforms.

The finite affine group is a matrix group whose entries come from a finite field. A natural subgroup consists of those matrices whose entries all come from a subfield instead. In this paper, I will introduce intermediate sub- groups with entries from both the field and a subfield. I will also examine the representations of these intermediate subgroups as well as the branch- ing diagram for the resulting subgroup chain. This will allow us to create a fast Fourier transform for the group that uses asymptotically fewer opera- tions than the brute force algorithm.

Plusieurs familles de fonctions spéciales de plusieurs variables, appelées fonctions d'orbites, sont définies dans le contexte des groupes de Weyl de groupes de Lie simples compacts/d'algèbres de Lie simples. Ces fonctions sont étudiées depuis près d'un siècle en raison de leur lien avec les caractères des représentations irréductibles des algèbres de Lie simples, mais également de par leurs symétries et orthogonalités. Nous sommes principalement intéressés par la description des relations d'orthogonalité discrète et des transformations discrètes correspondantes, transformations qui permettent l'utilisation des fonctions d'orbites dans le traitement de données multidimensionnelles. Cette description est donnée pour les groupes de Weyl dont les racines ont deux longueurs différentes, en particulier pour les groupes de rang $2$ dans le cas des fonctions d'orbites du type $E$ et pour les groupes de rang $3$ dans le cas de toutes les autres fonctions d'orbites. / Several families of multivariable special functions, called orbit functions, are defined in the context of Weyl groups of compact simple Lie groups/Lie algebras. These functions have been studied for almost a century now because of their relation to characters of irreducible representations of Lie algebras, their symmetries and orthogonalities. Our main interest is the description of discrete orthogonality relations and their corresponding discrete transforms which allow the applications of orbit functions in the processing of multidimensional data. This description is provided for the Weyl group of different lengths of root, in particular groups of rank 2 for so-called $E-$orbit functions and of rank 3 for all the other families of special functions.

Neste trabalho apresentamos um novo método de compressão, com perda controlada de dados, que tem a vantagem de ter uma taxa significativa de compressão sem introduzir nenhuma perda superior a um parâmetro escolhido pelo usuário. Esta abordagem é uma abordagem mista, pois usa técnicas de compactação de dados tanto com perda quanto sem perda. Isto quer dizer que conseguimos um método que alia as vantagens da alta compressão, sem introduzir distorções indesejáveis nos dados. Mostramos como a massa de dados utilizada nos nossos estudos é obtida e a sua importância na prospecção de depósitos de hidrocarbonetos. É apresentado um levantamento bibliográfico com técnicas de compressão aplicadas a dados sísmicos tipicamente utilizadas em aplicações comerciais. Por fim, apresentamos os resultados da compressão utilizando o método em conjuntos de dados sísmicos reais. Para 1% de erro, os arquivos de dados sísmicos compactados passaram a ter algo próximo a 25% de seus tamanhos originais, o que representa um fator de compressão de aproximadamente 4 / This work presents a new compression method with controlled loss of data, which has the advantage of having a significant compression ratio without introducing to the data a loss higher than a parameter chosen by the user. This approach is a mixed approach, as it uses lossy and lossless data compression techniques. This means that we have achieved a method that combines the advantages of high compression without introducing undesirable distortions in the data. We show how the mass of data used in our studies is obtained and its importance in the exploration of hydrocarbon deposits. A literature review is presented with compression techniques applied to seismic data typically used in commercial applications. Finally, we present the results of compression using the method on real seismic data sets. For 1% error, the archives of seismic data now have close to 25% of their original size, which represents a compression factor of about 4

Monitoring of abnormal events in a distribution feeder by using a single technique is a challenging task. Many abnormal events can cause unsafe operation, including a high impedance fault (HIF) caused by a downed conductor touch ground surface, an incipient fault (IF) caused by partial breakdown to a cable insulation, and a circuit breaker (CB) malfunction due to capacitor bank de-energization to cause current restrikes. These abnormal events are not detectable by conventional protection schemes. In this dissertation, a new technique to identify distribution feeder events is proposed based on the complex Morlet wavelet (CMW) and on a decision tree (DT) classifier. First, the event is detected using CMW. Subsequently, a DT using event signatures classifies the event as normal operation, continuous and non-continuous arcing events (C.A.E. and N.C.A.E.). Additional information from the supervisory control and data acquisition (SCADA) can be used to precisely identify the event. The proposed method is meticulously tested on the IEEE 13- and IEEE 34-bus systems and has shown to correctly classify those events. Furthermore, the proposed method is capable of detecting very high impedance incipient faults (IFs) and CB restrikes at the substation level with relatively short detection time. The proposed method uses only current measurements at a low sampling rate of 1440 Hz yielding an improvement of existing methods that require much higher sampling rates.

Neste trabalho apresentamos um novo método de compressão, com perda controlada de dados, que tem a vantagem de ter uma taxa significativa de compressão sem introduzir nenhuma perda superior a um parâmetro escolhido pelo usuário. Esta abordagem é uma abordagem mista, pois usa técnicas de compactação de dados tanto com perda quanto sem perda. Isto quer dizer que conseguimos um método que alia as vantagens da alta compressão, sem introduzir distorções indesejáveis nos dados. Mostramos como a massa de dados utilizada nos nossos estudos é obtida e a sua importância na prospecção de depósitos de hidrocarbonetos. É apresentado um levantamento bibliográfico com técnicas de compressão aplicadas a dados sísmicos tipicamente utilizadas em aplicações comerciais. Por fim, apresentamos os resultados da compressão utilizando o método em conjuntos de dados sísmicos reais. Para 1% de erro, os arquivos de dados sísmicos compactados passaram a ter algo próximo a 25% de seus tamanhos originais, o que representa um fator de compressão de aproximadamente 4 / This work presents a new compression method with controlled loss of data, which has the advantage of having a significant compression ratio without introducing to the data a loss higher than a parameter chosen by the user. This approach is a mixed approach, as it uses lossy and lossless data compression techniques. This means that we have achieved a method that combines the advantages of high compression without introducing undesirable distortions in the data. We show how the mass of data used in our studies is obtained and its importance in the exploration of hydrocarbon deposits. A literature review is presented with compression techniques applied to seismic data typically used in commercial applications. Finally, we present the results of compression using the method on real seismic data sets. For 1% error, the archives of seismic data now have close to 25% of their original size, which represents a compression factor of about 4