Investigation of noise influence on calculation of fractal dimension

In this paper we investigate in details the influence of the noise intensity on the result of the fractal dimension calculation. The fractal dimension of multidimensional torus is considered as an analysis object. Sum of a number of harmonic signals with irrational ratio of their frequencies and noise signal allows to construct partially destructed torus. It is shown that the presence of the noise leads to increase of the fractal dimension. Value of the increase depends on the relation between noise intensity and harmonics intensity.