EXTRACTING SLOWLY VARYING SIGNALS FROM A CHAOTIC BACKGROUND

Abstract

We consider the problem of extracting a small signal embedded in a stronger chaotic background. Under the assumption that the desired signal is relatively slowly varying we are able to devise an algorithm which in simple tests can recover the signal to a reasonable accuracy when the ratio of amplitudes of signal to chaotic background is as low as 10−10:1 when the dynamics of the background is known and 10−5:1 when the dynamics has to be estimated from the mixed signal itself. Potential applications include diagnostic monitoring of vibrating machinery as well as noise reduction in a variety of scenarios.