Linear recursive filters and nonlinear dynamics

In this paper we investigate the effects of filtering a chaotic time series with a linear IIR filter. Using the Kaplan and Yorke conjecture it has been argued that such filtering can result in an increase in information dimension. Here we show that the filter dynamics induce an extended dynamical system and that this system possesses a globally attracting invariant graph over the base system. Using this framework we obtain sufficient conditions on the filter dynamics that guarantee that the dimension remains unchanged.