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

Abstract

Natural phenomena are represented by signals having multiple components with different frequencies and amplitudes. Frequency domain feature extraction supplies the ability to use highly efficient spectral estimation algorithms, allowing the identification of signal characteristics that would be inaccessible in other domains. However, the different spectral estimation methods lack a comprehensive study that clearly presents their pros and cons. This degree project aims to prove the advantages and disadvantages of the parametric AR method using the Yule-Walker Algorithm, in comparison with the non-parametric method based on the simple and modified periodogram. This will be achieved through a detailed study and implementation of both methods. For the development of this project, a brief description of the classification and operation of the spectral estimation methods to be compared will be provided. Additionally, a step-bystep example will be presented, covering the calculation process from obtaining the model coefficients using the Yule-Walker algorithm to the spectral estimation of the parametric AR model. Then, this knowledge will be applied in the method, where several codes will be implemented and used for calculating the spectral estimation of the different methods. Additionally, a specifically developed code called 'mi_yule' will be used with the purpose of creating educational materials that ease the understanding of the Yule-Walker algorithm. As a result of this method, we intend to compare these methods through four tests that will allow us to discern the pros and cons of each one. These tests will enable us to evaluate the accuracy of amplitude estimation, frequency resolution, analyze computational load, and see the performance of the methods against AWGN noise.