Numerical and experimental investigation of the effect of filtering on chaotic symbolic dynamics

Motivated by the practical consideration of the measurement of chaotic signals in experiments or the transmission of these signals through a physical medium, we investigate the effect of filtering on chaotic symbolic dynamics. We focus on the linear, time-invariant filters that are used frequently in many applications, and on the two quantities characterizing chaotic symbolic dynamics: topological entropy and bit-error rate. Theoretical consideration suggests that the topological entropy is invariant under filtering. Since computation of this entropy requires that the generating partition for defining the symbolic dynamics be known, in practical situations the computed entropy may change as a filtering parameter is changed. We find, through numerical computations and experiments with a chaotic electronic circuit, that with reasonable care the computed or measured entropy values can be preserved for a wide range of the filtering parameter.