Extracting weak harmonic signals from strong chaotic interference

A new method of extracting weak harmonic signals from chaotic interference is described in this paper. In this method, the received time series is assumed to be composed of some kind of an unknown chaotic signal and very weak harmonics. Thus, the local-geometric-projection method of noise reduction for a chaotic signal can be applied, and, as a result, the purified chaotic signal and the residual error sequences are obtained. The residual error sequences contain most of the weak signals and are modeled as an autoregressive moving average process, and frequencies of the harmonics are resolved. The principles of the approach and the algorithm employed are described in detail. The optimal selection of the algorithm parameters such as the length of the received data, the embedding dimension, and the number of nearest-neighbor points are also discussed. Some simulations of extracting the weak signals with various amplitudes and frequencies from strong chaotic interference are made. Excellent results are achieved from these computer simulations indicating the high effectiveness of the approach.