Signals with an Additive Fractal Structure for Information Transmission

Signals with an Additive Fractal Structure for Information Transmission

M. V. Kapranov (Moscow Power Engineering Institute, Russia) and A. V. Khandurin (Moscow Power Engineering Institute, Russia)
DOI: 10.4018/978-1-4666-2208-1.ch005
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This chapter is devoted to a new class of wideband signals with an additive fractal structure. Properties and characteristics of the new type of signals are studied. It is shown that such signals possess a high level of an irregularity and unpredictability at simple technical implementation. It is shown that an incommensurability of frequencies of fundamental high-stable oscillations leads to the high level of an irregularity of such signals. For an estimation of a level of signal complexity, authors offer to use the fractal dimensionality of their temporal implementations calculated by means of creation of the structural function. Methods of modification of the signal spectrum with the additive fractal structure are offered, permitting to increase the efficiency of the frequency resource application. For reduction of the high low-frequency signal power the authors suggest using signals with the additive fractal structure, centered in a moving average window. Methods of masking of the voice messages by means of signals of a new type are offered. The results of a computer experiment of secretive sound transmission are described.
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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:


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