Effect of linear and nonlinear filters on multifractal analysis

In this paper we investigate how various linear and nonlinear transformations affect the multifractal properties of both artificial and traffic signals, using the multifractal analysis based on partition function, with comparison with the multifractal detrended fluctuation analysis. Specifically, we study the effect of three types of transforms which are often encountered in physical and biological processes: linear, nonlinear polynomial, and logarithmic filters. We compare the multifractal scaling properties of signals before and after the transform. It is shown that linear filters do not change the multifractal properties, while the effect of nonlinear polynomial depends on the power of the polynomial filter. In addition, the maximum value of the multifractal spectrum remains almost unchanged after the logarithmic filter. However, we find that the width of the multifractal spectrum changes significantly even for much smaller value of the offset parameter.