FEATURES OF SIMULATION OF CONFIDENTIAL INFORMATION TRANSMISSION SYSTEMS BASED ON PSEUDO-RANDOM SIGNALS OF MULTI-SCROLL SYSTEM

The paper investigates the features of modeling confidential information transmission systems based on the effects of dynamic chaos in multi-scroll systems. Recommendations for the choice of parameters of a multi-scroll system used in information transmission based on pseudo-random signals of a discrete-nonlinear system according to the Jerk circuit are obtained.

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.

Sparse Representations of Random Signals

Sparse (fast) representations of deterministic signals have been well studied. Among other types there exists one called adaptive Fourier decomposition (AFD) for functions in analytic Hardy spaces. Through the Hardy space decomposition of the $L^2$ space the AFD algorithm also gives rise to sparse representations of signals of finite energy. To deal with multivariate signals the general Hilbert space context comes into play. The multivariate counterpart of AFD in general Hilbert spaces with a dictionary has been named pre-orthogonal AFD (POAFD). In the present study we generalize AFD and POAFD to random analytic signals through formulating stochastic analytic Hardy spaces and stochastic Hilbert spaces. To analyze random analytic signals we work on two models, both being called stochastic AFD, or SAFD in brief. The two models are respectively made for (i) those expressible as the sum of a deterministic signal and an error term (SAFDI); and for (ii) those from different sources obeying certain distributive law (SAFDII). In the later part of the paper we drop off the analyticity assumption and generalize the SAFDI and SAFDII to what we call stochastic Hilbert spaces with a dictionary. The generalized methods are named as stochastic pre-orthogonal adaptive Fourier decompositions, SPOAFDI and SPOAFDII. Like AFDs and POAFDs for deterministic signals, the developed stochastic POAFD algorithms offer powerful tools to approximate and thus to analyze random signals.