Attractor reconstruction from filtered chaotic time series

Abstract

We present a method that allows one to decide whether an apparently chaotic time series has been filtered or not. For the case of a filtered time series we show that the parameters of the unknown filter can be extracted from the time series, and thereby we are able to reconstruct the original time series. It is demonstrated that our method works and provides reliable values of the fractal dimensions for systems that are described by maps or differential equations and for real experimental data.