Recursive filters driven by chaotic signals

Recursive filters are widely used in many practical signal processing and communications systems. Examples include both linear infinite impulse response filters (IIR) and recursive least squares (RLS) filters. Given the recent interest in chaotic time series it is topical to ask how such filters behave if driven by a signal generated by a deterministic nonlinear dynamical system. One would expect to see interesting effects due to the interaction between the driving dynamics and the filter's own natural dynamical behaviour. Such effects can have a profound influence on the performance of the filter and their explanation requires an understanding both of traditional signal processing techniques and of recent approaches to time series based on nonlinear dynamics. In this paper we outline the appropriate framework for studying such driven filters, give an outline of existing results for the IIR filter and explain how this may extended to the RLS algorithms. >