基于类洛伦茨系统的微弱信号检测及其电路实现

Detection of weak signals and circuit implementation based on similar Lorenz system

基于一种类洛伦茨(Lorenz)混沌系统,利用周期微扰的混沌控制方法,应用于微弱信号的检测。首先,构建一个受控的类Lorenz检测系统,通过调节系统两参数可将混沌系统控制可在所期望的周期轨道内。利用李雅普诺夫(Lyapunov)指数谱及分岔图分析,选择适当的两个参数值,将系统控制在混沌临界状态,当加入混有高斯白噪声的微弱信号时,系统发生相变,由混沌临界状态转变为周期三状态,从而检测出与外加激励信号同频率的微弱正弦信号。此方法不需要利用梅尔尼科夫(Melnikov)方法计算复杂的系统发生相变的激励信号幅值的精确解,实现方法简单易行,MATLAB仿真结果表明该系统可以实现极低的信噪比。在理论和数值分析的基础之上,该文设计了微弱信号检测电路,仿真和实验结果表明,该方法能够有效实现微弱正弦信号的检测。

The method of parameters of the periodic perturbation based on similar Lorenz system detect the weak signal with the application of chaos ,First of all, we construct a dominated similar Lorenz System and control the system in a particular periodical state by adjusting the two system＇s parameters.Then we use the Lyapunov exponential spectrum and the bifurcation diagram of the system, choose the two suitable parameters to control the system in the chaotic critical state,add the weak signal with the gauss white noise to the system.the system state change from the critical state to the periodical three state so that we can detect the weak periodical signal which has the same frequency as the driving signal. This method which is simple and easy to apply needn＇t calculate the accutate solution of Melnikov method. The results of simulation indicates that the similar Lorenz system could achieve extremely low SNR. The article designs the weak signal detection circuit by the theory and numerial＇s analysing to make the detection of weak sinusoidal signal come true.