Abstract / truncated to 115 words (read the full abstract)

This dissertation is concerned with the application of the theory of rational functions in signal processing. The PhD thesis summarizes the corresponding results of the author’s research. Since the systems of rational functions are defined by the collection of inverse poles with multiplicities, the following parameters should be determined: the number, the positions and the multiplicities of the inverse poles. Therefore, we develop the hyperbolic variant of the so-called Nelder–Mead and the particle swarm optimization algorithm. In addition, the latter one is integrated into a more general multi-dimensional framework. Furthermore, we perform a detailed stability and error analysis of these methods. We propose an electrocardiogram signal generator based on spline interpolation. It turns to be ... toggle 13 keywords

rational functions – malmquist-takenaka systems – discrete rational orthogonal systems – numerical algorithms in matlab – hyperbolic optimizations (nelder--mead – PSO – MDPSO) – ecg signal generator – qrs modeling – ecg compression – ecg quality measures – eeg signal modeling – epileptic seizure classification.

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