The purpose of this paper is to detect the periodic signal under strong noise background, and estimate its amplitude/phase.
Melnikov method is adopted as calculating the threshold value when chaos occurs, and the detected signal is taken as a system parameter. The system's output state is changed if the parameter has a slight change near the threshold. Meantime, the phase of system's output is recognized to judge whether the output state changes, and the signal parameter is estimated according to the necessary condition.
A small periodic signal in noise can be detected by Duffing oscillator via a transition from chaotic motion to periodic motion.
The paper shows how to calculate the amplitude/phase in low signal‐to‐noise ratios.
The Duffing system is sensitive to the weak periodic signal and has definite immunity to noise, so it is easy to construct a system composed of many oscillators that could process complex signals, even though the environmental noise is intense.
This paper presents a nonlinear method for detecting and extracting the weak signal.
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