El aporte principal de esta tesis es la de nición de wavelets sobre grillas tetraédricas no anidadas, lo que permite representar funciones de nidas sobre una tetraedrización irregular dada. La aplicación inmediata es la posibilidad de representar distintos atributos de nidos sobre un objeto como pueden ser su color, su brillo, su densidad, etc. En general, un objeto 3D admite una representación mediante una red tetraédrica no anidada sobre la cual están de nidas algunas propiedades del objeto. Esta representaci ón consiste de un conjunto de coe cientes correspondientes a una aproximación gruesa seguida por una sucesión de coe cientes de detalle que, en el caso clásico, miden el error entre dos aproximaciones sucesivas. En esta tesis se hallan la matriz de análisis que permite pasar de una resolución fina a una más gruesa y la de síntesis, necesaria para pasar de una resolución gruesa a una más fina, todo en el marco de grillas tetraédricas no anidadas. En este trabajo se resuelve entonces el problema que se presenta en Computación Gráfica cuando se quiere representar alguna propiedad que posee un objeto representado por una grilla que se reina de manera irregular. Para ilustrar esta aplicación se desarrolla un ejemplo en el cual se define un operador proyección sobre una tetraedrización dada y se hallan las matrices de análisis y de síntesis para dos resoluciones consecutivas. / The main contribution of this thesis is the definition of wavelets over non nested tetrahedral grids, allowing the representation of functions defined on an irregular tetrahedrization. In this way, it is possible to represent diferent attributes of a 3D object such as its color, brightness, density, etc. In general, a 3D object can be represented using a non nested tetrahedral grid over which some of its properties are defined. This representation consists of a set of coef- ficients corresponding to a coarse resolution followed by a set of detail coeficients that measure the error between two successive approximations in the classic wavelet theory. In this thesis the analysis matrix that allows going from a fine to a coarser resolution and the synthesis matrix needed for going from a coarse resolution to a finer one, are found. All this is within the framework of non nested tetrahedral grids. In this work is then completely solved the problem that appears in Graphic Computing when it is desired to represent a property of a given 3D object modeled by a tetrahedral grid irregularly refined. In order to illustrate the developed work, an example of a projection operator defined over an irregular tetrahedrization, together with the analysis and synthesis matrices that allow going from one resolution to the next are given.

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This study introduces new families of wavelets. The first is directly derived from the response of Second Order Underdamped Linear-Time-Invariant (SOULTI) systems, while the second is a generalization of the first to the complex domain and is similar to the Laplace transform kernel function. The first takes the acronym of SOULTI wavelet, while the second is named the Laplace wavelet. The most important criteria for a function or signal to be a wavelet is the ability to recover the original signal back from its continuous wavelet transform. It is shown that it is possible to recover back the original signal once the SOULTI or the Laplace wavelet transform is applied to decompose the signal. It is found that both wavelet transforms satisfy linear differential equations called the reconstructing differential equations, which are closely related to the differential equations that produce the wavelets. The new wavelets can have well defined Time-Frequency resolutions, and they have useful properties; a direct relation between the scale and the frequency, unique transform formulas that can be easily obtained for most elementary signals such as unit step, sinusoids, polynomials, and decaying harmonic signals, and linear relations between the wavelet transform of signals and the wavelet transform of their derivatives and integrals. The defined wavelets are applied to system analysis applications. The new wavelets showed accurate instantaneous frequency identification and modal decomposition of LTI Multi-Degree of Freedom (MDOF) systems and it showed better results than the Short-time Fourier Transform (STFT) and the other harmonic wavelets used in time-frequency analysis. The modal decomposition is applied for modal parameters identification, and the properties of the Laplace and the SOULTI wavelet transforms allows analytical and accurate identification methods. / Ph. D.

International Telemetering Conference Proceedings / October 23-26, 2000 / Town & Country Hotel and Conference Center, San Diego, California / Compressed video is necessary for a variety of telemetry requirements. A large number of competing video compression algorithms exist. This paper compares the ability of these algorithms to meet criteria which are of interest for telemetry applications. Included are: quality, compression, noise susceptibility, motion performance and latency. The algorithms are divided into those which employ inter-frame compression and those which employ intra-frame compression. A video tape presentation will also be presented to illustrate the performance of the video compression algorithms.

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This thesis presents a new preconditioner for elliptic PDE problems on unstructured meshes. Using ideas from second generation wavelets, a multi-resolution basis is constructed to effectively compress the inverse of the matrix, resolving the sparsity vs. quality problem of standard approximate inverses. This finally allows the approximate inverse approach to scale well, giving fast convergence for Krylov subspace accelerators on a wide variety of large unstructured problems. Implementation details are discussed, including ordering and construction of factored approximate inverses, discretization and basis construction in one and two dimensions, and possibilities for parallelism. The numerical experiments in one and two dimensions confirm the capabilities of the scheme. Along the way I highlight many new avenues for research, including the connections to multigrid and other multi-resolution schemes.

In this thesis, a wavelet-based prediction method is developed for concealing packet-loss effects in wireless channels. The proposed method utilizes a wavelet decomposition algorithm in order to process the data and then applies the well known linear prediction technique to estimate one or more approximation coefficients as necessary at the lowest resolution level. The predicted sample stream is produced by using the predicted approximation coefficients and by exploiting certain sample value patterns in the detail coefficients. In order to test the effectiveness of the proposed scheme, a wireless channel based on a three-state Markov model is developed and simulated. Simulation results for transmission of image and speech packet streams over a wireless channel are reported for both the wavelet-based prediction and direct linear prediction. In all the simulations run in this work, the wavelet-based method outperformed the direct linear prediction method. / Hellenic Navy author.

The main objective of the thesis is to analyse impact of wavelet covariance estimation in the context of Markowitz mean-variance portfolio selection. We use a rolling window to apply maximum overlap discrete wavelet transform to daily returns of 28 companies from DJIA 30 index. In each step, we compute portfolio weights of global minimum variance portfolio and use those weights in the out-of- sample forecasts of portfolio returns. We let rebalancing period to vary in order to test influence of long-term and short-term traders. Moreover, we test impact of different wavelet filters including Haar, D4 and LA8. Results reveal that only portfolios based on the first scale wavelet covariance produce significantly higher returns than portfolios based on the whole sample covariance. The disadvantage of those portfolios is higher riskiness of returns represented by higher Value at Risk and Expected Shortfall, as well as higher instability of portfolio weights represented by shorter period that is required for portfolio weights to significantly differ. The impact of different wavelet filters is rather minor. The results suggest that all relevant information about the financial market is contained in the first wavelet scale and that the dynamics of this scale is more intense than the dynamics of the whole market.

Wavelets são descritas como sendo capazes de dar tanto resolução em frequência como resoluçãao temporal a um sinal. Este trabalho revisa o que e o domínio da frequência em um espa co de dimensão nita, como o RN e apresenta como a Transformada Wavelet Discreta e a Maximum Overlap Discrete Wavelet Transform podem ser usadas para decompor um sinal em diversos componentes de escalas, que podem ser vistos como componentes de frequência ou componentes temporais. Então uma aplicação para a estimação do núcleo de inflação para o IPCA oficial brasileiro e apresentada. Ela consiste em obter uma Análise Multirresolução baseada na wavelet Daubechies 2 e estimar a inflação subjacente, ou removendo-se níveis detail, ou aplicando um algoritmo de threshold. Por ultimo, alguns testes de qualidade de medida sugeridos pela literatura são executados. Isso e feito com o conjunto completo dos dados e com um conjunto restrito, obtido com um método baseado em wavelets para detecção de quebras estruturais em séries temporais. / Wavelets are described as being able to give both a time resolution and a frequency resolution to a signal. This work reviews what is the frequency domain when represented by a nite dimensional space such as the RN and presents how the Discrete Wavelet Transform and the Maximum Overlap Discrete Wavelet Transform can be used to decompose a signal in several scale components, which can be viewed as frequency components or as time components. Then an application to the estimation of the core in ation for the o cial Brazilian CPI is presented. This is done by obtaining a Multi Resolution Analysis based on the Daubechies 2 wavelet and estimating the underlying in- ation rate by either removing detail levels completely or applying a threshold algorithm. Lastly, a few tests of quality of measurement proposed by the literature are performed. This is done with the full set of data and a restricted set, obtained with a wavelet method for detecting structural breaks in time series.

by Lau Shui-kong, Francis. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 95-98). / Abstracts in English and Chinese. / Chapter 1 --- General Theory of Wavelets --- p.8 / Chapter 1.1 --- Introduction --- p.8 / Chapter 1.2 --- Multiresolution Analysis and Wavelets --- p.9 / Chapter 1.3 --- Orthonormal Bases of Compactly Supported Wavelets --- p.12 / Chapter 1.3.1 --- Example : The Daubechies Wavelets --- p.15 / Chapter 1.4 --- Wavelets in Higher Dimensions --- p.20 / Chapter 1.4.1 --- Tensor product method --- p.20 / Chapter 1.4.2 --- Multiresolution Analysis in Rd --- p.21 / Chapter 1.5 --- Generalization to frames --- p.25 / Chapter 2 --- Wavelet Bases Numerical Algorithm --- p.27 / Chapter 2.1 --- The Algorithm in Wavelet Bases --- p.27 / Chapter 2.1.1 --- Definitions and Notations --- p.28 / Chapter 2.1.2 --- Fast Wavelet Transform --- p.31 / Chapter 2.2 --- Wavelet-Based Quadratures --- p.33 / Chapter 2.3 --- "The Integral Operator, Standard and Non-standard Form" --- p.39 / Chapter 2.3.1 --- The Standard Form --- p.40 / Chapter 2.3.2 --- The Non-standard Form --- p.41 / Chapter 2.4 --- The Calderon-Zygmund Operator and Numerical Cal- culation --- p.45 / Chapter 2.4.1 --- Numerical Algorithm to Construct the Non- standard Form --- p.45 / Chapter 2.4.2 --- Numerical Calculation and Compression of Op- erators --- p.45 / Chapter 2.5 --- Differential Operators in Wavelet Bases --- p.48 / Chapter 3 --- T(l)-Theorem of David and Journe --- p.55 / Chapter 3.1 --- Definitions and Notations --- p.55 / Chapter 3.1.1 --- T(l) Operator --- p.56 / Chapter 3.2 --- The Wavelet Proof of the T(l)-Theorem --- p.59 / Chapter 3.3 --- Proof of the T(l)-Theorem (Continue) --- p.64 / Chapter 3.4 --- Some recent results on the T(l)-Theorem --- p.70 / Chapter 4 --- Singular Values of Compact Pseudodifferential Op- erators --- p.72 / Chapter 4.1 --- Background --- p.73 / Chapter 4.1.1 --- Singular Values --- p.73 / Chapter 4.1.2 --- Schatten Class Ip --- p.73 / Chapter 4.1.3 --- The Ambiguity Function and the Wigner Dis- tribution --- p.74 / Chapter 4.1.4 --- Weyl Correspondence --- p.76 / Chapter 4.1.5 --- Gabor Frames --- p.78 / Chapter 4.2 --- Singular Values of Lσ --- p.82 / Chapter 4.3 --- The Calderon-Vaillancourt Theorem --- p.87 / Chapter 4.3.1 --- Holder-Zygmund Spaces --- p.87 / Chapter 4.3.2 --- Smooth Dyadic Resolution of Unity --- p.88 / Chapter 4.3.3 --- The proof of the Calderon-Vaillancourt The- orem --- p.89 / Bibliography