Estimation of the Distribution Probability Density Acoustic Signals And Interferences, the Reconstruction Methods

Abstract

In operation, methods of estimating probability density distributions are considered, which are urgent in the solution of the filtering issues of the useful information on the background of external acoustic noise in the telecommunications systems. Parametric and non-parametric methods of estimating probability densities are discussed, methods for determining an empirical distribution function for the case of a limited sample volume. It is shown that the approximation of the probabilities empirical data can be performed by the method of nuclear evaluations. Within this method, the estimate may be represented by the convolution of the core and the empirical density. It derives from the fact that the nuclear score is a result of a histogram of the histogram evaluation. It has been shown that reconstruction of the distribution function as a polynomial in the system of functions is the question of finding coefficients, which is the task of linear regression, which is solved by minimisation of the quadratic function of the loss built on the basis of the use of the least-squares method and representing the discrepancy of the empirical data and the estimates obtained on their basis. The results of the experimental studies show the error of the reconstruction one-dimensional function of probability density for the case of audio signals and acoustic interferences, given different kinds and orders of polynomial approximation.