Power spectrum densities, probability density functions and correlation functions of the fractal Brownian signal (FBS) are studied with the aim of MATLAB simulation. The influence of a time-scaling factor on these properties is investigated. Particularly, the increase of this factor leads to increasing the influence of the Hurst index on power spectrum density. The results are conformed to Mandelbrot’s investigations of FBS properties.
- N. Starchenko, “The index of the fractal and local analysis of chaotic time series,” Ph.D. dissertation, Moscow, Russia, 2005. (Russian)
- V. Fomin, “Statistical analysis of ip and voip traffic”, Infokommunikatsionnyie tekhnologii, vol. 7, no. 1, pp. 40-44, Moscow, Russia, 2009. (Russian)
- K. Vasyta “Method of information transfer, based on the manipulation of the Hurst index of fractal ("color") Gaussian noise”, Systemy obrobky informatsii, vol. 6, no 1, pp. 62-65, Kharkiv, Ukraine: Ivan Kozhedub Kharkiv University of Air Forces, 2010. (Russian)
- K. Vasyta, S. Ozerov, and A. Korolyk, “Features of construction of steganographic radio systems”, Problemi telecommunikasiy, vol. 8, no. 3, pp. 94-104, Kharkiv, Ukraine: Ivan Kozhedub Kharkiv University of Air Forces, 2012. (Russian)
- B. Romanov, S. Krasnov, The theory of electrical connections. Messages, signals, interference, their mathematical models: a training manual. Ulyanovsk, Russia, 2008 (Russian).
- V. Bolotov, et al., “Fractal Communication System”, Electromagnetic Phenomena , vol. 7, no. 18, pp. 174–179, Kharkiv, Ukraine: Institute for Electromagnetic Research, 2008.
- M. Klymash, R. Politanskyy, “Cluster coding”, Eastern-European Journal of Enterprise Technologies, vol. 59, no. 5/3, pp. 50-54, Kharkiv, Ukraine, 2012. (Ukrainian)
- O. Moskalenko, A. Koronovskii, E. Hramov, “Generalized synchronization of chaos for secure communication: Remarkable stability to noise”, Physics Letters A, no. 374, pp. 2925-2931, Amsterdam, Netherlands: Elsevier, 2010.
- L. Ivolga, L. Politanskyy, R. Politanskyy, “Precision oscillator chaos in invariant communication systems”, Problemy telekomunikatsiy, vol. 1, no. 3, pp. 106-116, Kharkiv, Ukraine: Ivan Kozhedub Kharkiv University of Air Forces, 2011. (Ukrainian)
- J. Feder, Fractals. New York, USA: Plenum Press, 1991.
- B. Mandelbrot, J. Wallis, “Computer experiments with fractional Gaussian noises. Part 1, Averages and variances”, Water Resour. Res., no. 5, pp. 228-241, New York, USA: American Geophysical Union, 1969.