Francisco Villarreal

Colombeau's theory and shock waves in a problem of hydrodynamics

Instituto de Matematica e Estatistica Universidade de Sao Paulo, Caixa Postal 20570, Sao Paulo

Composition and invertibility for a class of generalized functions in the Colombeau's theory

In this work we define the composite function for a special class of generalized mappings and we study the invertibility for a certain class of generalized functions with real values.

A state-space description for perfect-reconstruction wavelet FIR filter banks with special orthonormal basis functions

This paper presents a state space description for wavelet FIR filter banks with perfect reconstruction using special orthonormal basis functions. The FIR structure guarantees the BIBO stability, robustness and improves the filter divergence problem while orthonormal basis functions have characteristics that make them attractive in the modeling of dynamic systems. The state space description presented in this paper has all of those advantages and is minimal.

ANÁLISE DE MÉTODOS DE INSERÇÃO E EXTRAÇÃO DE MARCA D'ÁGUA NO DOMÍNIO WAVELET

Este trabalho analisa o desempenho de tres tecnicas existentes cujos resultados na manipulacao de marca d’agua sao satisfatorios. A primeira tecnica a ser analisada e a proposta por Cox et al. [4]. Esta tecnica e uma das pioneiras neste assunto e usa da transformada discreta de cossenos (DCT) na decomposicao da imagem hospedeira. A segunda tecnica e mais evoluida, trabalha com uma marca d’agua binaria, porem aleatoria, e faz a decomposicao da imagem usando a transformada wavelet discreta (DWT), tal metodo foi proposto por Joo et al. [5]. E, por ultimo, o metodo proposto Hajjara et al. [6] que trata a marca d’agua como sendo uma imagem binaria e aplica a transformada wavelet usando funcoes biortogonais.

Heaviside generalized functions and shock waves for a Burger kind equation

The purpose of the work is to study the existence and nonexistence of shock wave solutions for the Burger equations. The study is developed in the context of Colombeaus theory of generalized functions (GFs). This study uses the equality in the strict sense and the weak equality of GFs. The shock wave solutions are given in terms of GFs that have the Heaviside function, in x and (x, t) variables, as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function, in ℝ n and ℝ n ×ℝ, in the distributional limit sense.

Composition for a class of generalized functions in Colombeau's theory

In Colombeaus theory, given an open subset , there is a differential algebra of generalized functions which contains in a natural way the space of distributions as a vector subspace. There is also a simpler version of the algebra .Although this subalgebra does not contain, in canonical way, the space is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

Polinômios com Coeficientes de Fibonacci e Wavelets

Neste trabalho, considera-se uma funcao racional cujo numerador e denominador sao polinomios com coeficientes de Fibonacci. O principal objetivo e mostrar que a derivada quarta dessa funcao obtida a partir dos polinomios com coeficientes de Fibonacci e uma funcao wavelet.

A comparative study between recent wavelet nonthresholding methods and the well-established spectral subtractive and statistical-model-based algorithms for speech enhancement under real noisy conditions

In this paper, a comparative study between current wavelet nonthresholding methods for speech enhancement and the well-established spectral subtractive and statistical-model-based algorithms is performed. The development and evaluation of speech enhancement methods is essential in many branches of telecommunications and entertainment industry. Two classes of speech enhancement methods encompassing both, DFT and wavelet based methods, are evaluated and faced with the current wavelet nonthresholding schemes. Objective analysis taking into account various real noise environments are presented. Questions about wavelet thresholding performance on real noisy environments are discussed. Objective evaluations considering SNR improvement, correlation among original and enhanced sentences and PESQ scores shown that nonthresholding schemes overcome totally the wavelet thresholding methods in PESQ scores, besides performing equally well in noise suppression. A second objective is the identification, among the considered methods, of the more suitable to certain kind of real noisy conditions.

Dual-Tree Complex Wavelet Transform in the problem of speech enhancement

The dual-tree complex wavelet transform is considered a relatively recent improvement for the discrete wavelet transform. In this paper, the applicability of such transform in the problem of speech enhancement is evaluated. For this purpose, a nonthreshold scheme is proposed. Two filters, one for the imaginary part and other for the real part of complex wavelet coefficients were designed. These two real filters were then averaged to obtain the final filter. A uniform noise reduction was performed for all wavelet scales. Simulation results show that, together, nonthresholding scheme and dual-tree complex wavelet transform obtained consistently results.

UM MÉTODO PARA CODIFICAÇÃO DE IMAGENS DIGITAIS NO DOMÍNIO WAVELET

Com objetivo de economiza espaco para armazenamento, este trabalho apresenta um metodo de codificacao de imagens digitais que passam a ser representadas em um vetor de codificacao. A ferramenta de apoio para um melhor resultado na compressao dos dados e a Transformada Wavelet (TW). Tal ferramenta tem apresentado resultados satisfatorios ao lidar com sinais bidimensionais se tratando de codificacao e decodificacao devido sua caracteristica marcante de multirresolucao [1].