The Use of Fractal Signals in Information and Communication Systems

Abstract

A mathematical model for the formation of a fractal signal based on van der Pol non-linear differential equations is proposed. The formation of the structure of fractal signals is based on the self-similarity hypothesis, which allows an infinite series of embedding identical (homeomorphic) vibrations into each other. The property of hyperbolicity in the formation of a fractal signal using reference harmonic oscillations is to compress (decrease) the amplitude and stretch (increase) the frequency. Based on models of a fractal signal, it is possible to build forming signals with variable parameters. The fundamental possibility of using a fractal signal as an information signal carrier, i.e. a fractal signal is used as a masking signal. The parameters of the fractal signal are agreed (selected) with the participation of all interested parties. The fractal carrier signal has a wider range of parameters, which, in addition to amplitude, frequency and initial phase, include: the scaling factor (similarity), as well as the number and parameters of harmonic components involved in the formation of the signal. The specific parameters and properties of a fractal signal that distinguish it from classical radio signals allow it to be used to increase the availability of transmitted information. The fractal signal allows the generators to be identical on the receiving side of the system.