Pylypenko K. Statistics analyzer and classifier of speech signals based on the mixture of Gaussian distributions

The thesis is devoted to theoretical justification of the use of a mixture of Gaussian distributions as a model for the probability density of the speech signals. Investigated the distribution function of two-component mixtures and obtained Gaussian solution of identification probability densities. The author obtained solution of the identification equation for the probability density that allow one to find the parameters of the mixture by known cumulant coefficients of the random variable and formulated method and a program of identification probability densities using a two-component mixture of Gaussian distribution. The analytical expression for the variance of the estimations of the parameters of mixture distribution and variance of the estimations of the distribution are obtained. The use of the cumulant coefficients of speech signal as the classification criteria for solving identification problem is proposed. The method for speaker's gender identification based on cumulant coefficients of speech signal is proposed and classification errors are analyzed.