AproximaÃÃo espectral e construÃÃo de wavelets com aplicaÃÃes em eletrogastrografia / Spectrum approximation and wavelet design with applications in electrogastrography

AUTOR(ES)
DATA DE PUBLICAÇÃO

2005

RESUMO

Signal analysis is one of the most important areas of Signal Processing. This thesis is divided in three parts, each one addressing a specific topic of signal analysis. The sub-areas were: (i) approximate methods for spectrum evaluation; (ii) wavelet design; and (iii) biomedical signal analysis. The problem of spectrum estimation under constraints of minimal computational complexity was addressed by means of approximation methods. The first proposed procedure was the Rounded Hartley transform, which utilizes the round-off function to generate a transformation matrix of null multiplicative complexity. The second introduced method was the arithmetic Hartley transform. The major role of interpolation in arithmetic transform theory was demonstrated. Moreover, interpolation schemes for Hartley, Fourier cosine and Fourier sine transform were suggested. The emphasis was then directed to wavelet design. Two new approaches were examined: (i) designing new wavelets from differential equations; and (ii) designing matched optimal wavelets for a given class of signals. The first methodology furnished the definition of two new wavelets: the Mathieu wavelets (based on Mathieu functions) and the Chebyshev wavelets (based on Chebyshev polynomials). The properties of such wavelets were quantitatively investigated and potential applications were suggested. The second approach consisted of an algorithm for the determination of optimal wavelets to analyze electrogastrographic (EGG) signals. Arguments of error minimization of reconstructed compressed signals were invoked to determine optimal wavelet parameters. In the final part, an algorithm for the classification of EGG signals was formulated. It was sought the discrimination between gastric electrical uncoupling and basal groups

ASSUNTO(S)

electrogastrography spectrum approximation gastric electrical activity wavelet design construÃÃo de wavelets transformadas aritmÃticas approximate algorithms eletrogastrografia algoritmos aproximados atividade elÃtrica gÃstrica arithmetic transforms engenharia eletrica aproximaÃÃo espectral

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