Parametric time-frequency analysis for discrimination of non-stationary signals = [Análisis tiempo-frecuencia paramétrico para la discriminación de señales no estacionarias]

Abstract

Abstract: In this master�s thesis discrimination of non-stationary signals using time varying parametric modeling and time frequency analysis is explored. This work consists of two parts, the first, to obtain a representation for non-stationary signals by parametric modeling and parametric time-frequency representations, and the second, feature selection and extraction based on time�frequency representations and time-varying data. In this study many advantages of non-stationary signal analysis using parametric methodology will be made evident. Among them it will be found that by means of these models it is possible to determine how signal�s structure changes along time and analogously, to determine how the frequency content of a signal changes. The effectiveness of this methodology depends on three main factors, first, the choice of the model structure, which in the case of TVAR modeling would be the problem to find the order of AR model, second, estimation of the model parameters and third, selection the structure of temporal change that is imposed on the dynamics of time-variant parameters. In this aspect, a revision and evaluation of different state of the art methodologies for model structure selection, estimation of TVAR parameters and temporal structures is made. It was found that the performance of parametric methodology depends directly on these three factors; however, the main influencing factor is the structure of temporal change imposed on the estimator and how it couples with the dynamics of a time-varying signal. The second addressed problem is how to use these time varying features (matricial features) to train classifiers. Features estimated with parametric models yield a complete representation of signal�s dynamics at the cost of large dimensionality and redundancy. Thus, a review of feature extraction methods devised for time-varying and matricial data is carried out. Also, relevance analysis is generalized for the case of matricial data.