Analysis of the Transformation of Random Signals and Noise Using Poly-Gaussian Models

Analysis performed transformation of random signals and noise in linear and nonlinear systems based on the use of poly-Gaussian models and multidimensional PDF of the output paths of information-measuring and radio systems. The classification of elements of these systems, as well as expressions describing the input action and output response of the system are given. It is shown that the analysis of information-measuring and systems can be carried out using poly-Gaussian models. The analysis is carried out with a series connection of a linear system and a nonlinear element, a series connection of a nonlinear element and a linear system, as well as with a parallel connection of the named links. The output response in all cases will be a mixture of a poly-Gaussian distribution with a number of components. An example of the analysis of signal transmission through an intermediate frequency amplifier and a linear detector against a background of non-Gaussian noise is given. The resulting probability density distribution of the sum of the signal and non-Gaussian noise at the output of the detector will be poly-Rice. The multidimensional probability distribution density of the output processes of the nonlinear signal envelope detector is also obtained. The results of modeling the found distribution densities are presented. It is shown that the use of the poly-Gaussian representation of signals and noise, as well as the impulse response of the system, makes it possible to effectively analyze inertial systems in the time domain.