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.

No description available.

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

The ionosphere is a dynamic and ionized medium. Specification of the ionospheric electron density is important for radio systems operating up to a few GHz. Such systems include communication, navigation and surveillance operations. Computerized Ionospheric Tomography (CIT) is a technique that allows specification of the electron density in the ionosphere. CIT, unlike medical tomography, has geometric limitations such as uneven and sparse distribution of ground-based receivers and limited-angle observations. The inversion is therefore underdetermined and to overcome the geometric limitations of the problem, regularization techniques need to be used. In this thesis the horizontal variation of the ionosphere is represented using wavelet basis functions. Wavelets are chosen because the ground based ionospheric instrumentation is unevenly distributed and hence there is an expectation that the resolution of the tomographic image will change across a large region of interest. Wavelets are able to represent structures with different scale and position efficiently, which is known as Multi Resolution Analysis (MRA). The theory of sparse regularization allows the usage of a small number of basis functions with minimum loss of information. Furthermore, sparsity through wavelets can better differentiate between noise and actual information. This is advantageous because it increases the efficacy to resolve the structures of the ionosphere at different spatial horizontal scale sizes. The basis set is also extended to incorporate time dependence in the tomographic images by means of three-dimensional wavelets. The methods have been tested using both simulated and real observations from the Global Navigation Satellite System (GNSS). The simulation was necessary in order to have a controllable environment where the ability to resolve different scale structures would be tested. The further analysis of the methods required also the use of real observations. They tested the technique under conditions of temporal dynamics that would be more difficult to reproduce with simulations, which often tend to be valid in quiet ionospheric behaviors. Improvements in the detection and reconstruction of ionospheric structures were illustrated with sparse regularization. The comparison was performed against two standard methods. The first one was based on spherical harmonics in space, whilst the second relied on a time-dependent smoothing regularization. In simulation, wavelets showed the possibility to resolve small-scale structures better than spherical harmonics and illustrated the potential of creating ionospheric maps at high resolution. In reality, GNSS satellite orbits allow satellite to receiver datasets that traverse the ionosphere at a few hundred km per second and hence a long time window of typically half an hour may be required to provide observations. The assumption of an unchanging ionosphere is only valid at some locations under very quiet geomagnetic conditions and at certain times of day. For this reason the theory was extended to include time dependence in the wavelet method. This was obtained by considering two approaches: a time-smooth regularization and three-dimensional wavelets. The wavelet method was illustrated on a European dataset and demonstrated some improvements in the reconstructions of the main trough. In conclusion wavelets and sparse regularization were demonstrated to be a valid alternative to more standard methods.

A apneia é um Distúrbio Respiratório do Sono com grande incidência, estimando-se que esteja presente em 13% dos homens e 6% das mulheres nos Estados Unidos. Correlacionados com a apoeia, estão a obesidade, a diabete mellitus e, principalmente, algumas doenças cardíacas. No Brasil ainda há poucas pesquisas, possivelmente pelo difícil acesso e pelo alto custo das Polissonografias. Neste trabalho são analisados alguns sinais de Polissonografia, como o Eletrocardiograma, a Saturação do Oxigênio no Sangue, o Flu.xo Respiratório e o Esforço Respiratório. Mostramos como a Transformada Wavelet Discreta e as Redes Nemais constituem ferramentas matemáticas computacionais que possibilitam a extração de características e a classificação, servindo de suporte ao diagnóstico utilizado at ualmente. / Apnea is a highly incident Sleep-Disordered Breathing, which a icts roughly 13% of men and 6% of the women in the USA. It is also found a few correlations with other diseases, like obesity, diabetes mellitus and, especially, certain cardiac diseases. In Brazil, there are few studies, possibly due to the di cult access and the cost of Polysomnography. In this study, we analyzed some signals of Polysomnography, as the electrocardiogram, the oxygen saturation, the respiratory ow and respiratory e ort. We show how the Discrete Wavelet Transform and Neural Network may be applied as computational mathematical tools that enable feature extraction and classi cation, serving to support the diagnosis currently used.