Dimension increase in filtered chaotic signals

Abstract

An increase in fractal dimension is shown to occur in filtered chaotic signals. The dependence of the Lyapunov dimension on the filter parameters is used to predict the behavior of the information dimension which is directly evaluated for two experimental systems: the NMR laser and Rayleigh-B\'enard convection. Good quantitative agreement with the theoretical predictions is found. The understanding of the role of filtering not only clarifies aspects relevant in the calculation of fractal dimensions, but also yields an indirect but precise way of evaluating Lyapunov exponents.