Abstract: To the fractal profiles synthesized by discrete Fourier transform, the relationship between fractal parameters (fractal dimension D, scale factor C) and traditional parameters, the influence of fractal parameters on the geometric shape of profiles, and the influence of fractal parameters on filtering are studied respectively. It is found that if the power spectrum of a profile is assumed to fit the power law strictly, a quantitative relationship between fractal parameters and root mean square deviation can be established by Parseval theorem, but the rest of traditional parameters are still random and not linear related. Fractal dimension D influences the energy ratio between high frequency components and low frequency components of a profile. D increasing, the high frequency components of a profile are increased, which makes the geometric shape of a profile appear rougher. With the same fractal dimension, if the scale factor is larger, the root mean square deviation is larger. When a fractal profile is filtered to be smooth, more energy can be preserved in a profile with smaller D.

Key words: Discrete Fourier transform, Fractal geometry, Fractional Brownian motions