Detecting Weak Signal Based On The Duffing Chaotic Oscillator

Weak signal detection takes advantage of electronics, information theory and physics to detect the weak signal hidden in noise by analyzing the measured signal characteristics and relevance. Generally speaking, the traditional linear filtering detection is invalid on the background of stronger noise. Therefore, finding a new detection method is an urgent task. According to chaos theory, under certain conditions chaotic system is sensitive to small signal while immune to noise which have the potential for weak signal detection. So chaos system can be used to detect weak signals. In recent years, detection of weak signals using chaos system has been received considerable attention. This thesis detects the weak sinusoidal signal based on Duffing system, the main contents are as follows:1. We propose the method of using phase plane, timing sequence diagram and Lyapunov exponents to judge the threshold of Duffing system. We know the weak signal detection based on Duffing chaotic oscillator needs to set the exact threshold, because the threshold affects the precision of the test results. This thesis comprehensively uses three methods above to get a more accurate threshold of Duffing system and lays a solid foundation for the later on the contents of weak sinusoidal signal detection. Simulation results verify the effectiveness of the proposed method.2. In order to detect frequency of weaker sinusoidal signal, we adjust the parameters of Duffing system to make the threshold of Duffing system and the amplitude of weak sinusoidal signal at the same level. Furthermore, we make the threshold of Duffing system small by changing relative parameters of Duffing system, reduce the oscillator frequency ratio among oscillators, and increase the number of oscillators to get higher accuracy. Numerical simulation shows the effectiveness and accuracy of the proposed method.3. Because there is some deficiency of the current phase detection methods, this thesis proposes a new method on phase detection of weak sinusoidal signal based on the Duffing chaotic oscillator, namely, the phase oscillator array method. It assimilates the advantages of two coupled Duffing oscillator detection method and one-third phase detection method, abandons their shortcomings, ultimately obtains a convenient, much more precise and easy-to-project implemented method on phase detection of weak sinusoidal signals. It can also increase the number of phase oscillator to reduce the phase detection error, and have a certain immunity to noise. Simulation results verify the effectiveness of the proposed method.4. For the purpose of detect lower amplitude of weak sinusoidal signal based on Duffing chaotic oscillator, we adjust the parameters of the Duffing system again to make the system's threshold and amplitude of weak sinusoidal signal keep in the same order of magnitude. This method can effectively detect lower amplitude of sinusoidal signal, and make the amplitude detection more accurate and immune to interference. Numerical simulation verify the effectiveness of the proposed method.