Signals with an Additive Fractal Structure for Information Transmission

Main Characteristics Of Fractal Functions With An Additive Structure

Signals with a fractal structure can be divided into some types according to methods of their formation in the transmitter: signals with additive (Wornell, 1996, Falconer, 1997) and multiplicative (Bolotov & Tkach, 2006, pp.91-98) structure, signals on the basis of iterative fractal functions (Kravchenko, Perez-Meana, & Ponomaryov, 2009) (functions of Cantor, Bolzano, Bezikovich, etc.), solution of nonlinear dynamic systems in the reverse time (Tomashevsky & Kapranov, 2006). The main lack of almost all fractal signals is the impossibility of their generation in the form of self-oscillations in devices with the simple structure. However, fractal functions with an additive structure and signals on their basis, which are a sum of stable sinusoidal oscillations with incommensurable frequencies, can be obtained without the expensive equipment. Except fractal properties and simple generation methods, signals with an additive fractal structure demonstrate a high level of reproducibility. These properties can be used for secured telecommunications, therefore, the research of such signals is urgent and this chapter is devoted only to them.

On determination (for example Wornell (1996)), any fractal function should satisfy the following scaling equation: