Estudio y comparación de métodos de estimación espectral aplicados a una señal artificial : estudio de los fundamentos matemáticos e implementación del método paramétrico ar por medio del algoritmo de burg y su comparación con los métodos no paramétricos basados en fourier (periodograma simple y modificado).

Abstract

The present study faces the problem of the lack of publications about the comparison of spectral estimation methods. There are many spectral estimation methods, but unfortunately, there is no research that compares them based on an artificial signal. In addition, there are no investigations that face the problems of frequency resolution and the ability to detect components of very small amplitudes. These problems are common in traditional methods based on Fourier (simple and modified periodogram). In order to deal with this problem, a comparison is proposed between the Burg Algorithm, a parametric method, and periodogram (simple and modified), a non-parametric method. To achieve this, the mathematical and theoretical content about the algorithm was presented, in a didactic way. And then, the algorithm was implemented in Matlab step by step. Finally, the results obtained showed that Burg's parametric method achieved a high frequency resolution and an extraordinary ability to detect very small amplitude components. Although, it did not correctly find the amplitudes of the artificial signal. However, Burg's method achieved an advantage since it maintained a constant frequency resolution while the duration of the artificial signal was reduced. In contrast, periodogram experienced a decrease in its frequency resolution and its ability to detect components as the duration of the artificial signal decreased.