Smoothing non-smooth systems with low-pass filters

Abstract

Low pass filters, which are used to remove high frequency noise from time series data, smooth the signals they are applied to. In this paper we examine the action of low pass filters on discontinuous or non-differentiable signals from non-smooth dynamical systems. We show that the application of such a filter is equivalent to a change of variables, which transforms the non-smooth system into a smooth one. We examine this smoothing action on a variety of examples and demonstrate how it is useful in the calculation of a non-smooth system’s Lyapunov spectrum.