Research The Duffing Chaotic Oscillator And The Multi-frequency Weak Signal

Chaos theory has extensive applications in numerous fields, which demonstrates its superiority especially in the weak signal detecting. For traditional methods of detecting weak signal, it is difficult to further reduce the threshold of input Signal to Noise Ratio(SNR). And the useful signal can't be efficiently detected from the strong noise background. With the method of detecting weak signal based on chaos theory which broke the bottleneck of weak signal detection, weak signal can be detected in the extremely low SNR The main idea is as follows:the chaos system is sensitive to initial conditions and immune to noise. By using the change of the phase trajectory jumped from chaotic state to periodic state, the weak signal can be detected.Detected signal is usually composed of multi-frequency signals in many field, such as fault detecting, earthquake detecting and radar target detecting and so on. So its detection has great significance.Based on Duffing vibrator system, an improved method which is Wigner transformation-variance extremum joint multi-frequency sine signal frequency detection is proposed in this paper. Fistly, the approximation of each signal frequency is estimated by variance extremum method. Secondly, the frequency of the multi-frequency sine signal is estimated effectively by using Wigner distribution and Lebesgue measur, which can remove the misreading frequency and improve the accuracy of the approximation. The Matlab simulation results show that it is not only improving the accuration but also the precision of the detected signal.