Analysis of the geometric characteristic quantity of the periodic solutions of the chaotic oscillator system and the quantitative detection of weak periodic signal
Analysis of the geometric characteristic quantity of the periodic solutions of the chaotic oscillator system and the quantitative detection of weak periodic signal
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混沌振子系统周期解的几何特征量分析及微弱周期信号的定量检测
DOI：
10.7498/aps.57.3353
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发表时间：
2008-06
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本文提出了一种微弱周期信号的定量检测方法。在分析大尺度周期状态下混沌振子系统的稳定输出时得到的结果表明，混沌振子系统周期解的平均面积是混沌振子系统周期解的稳定几何特征量。平均面积与待检测幅度之间存在稳定且单调递增的关系。当定义一些参数时，几何特征量的精度可以达到10 -6 V 2 。微弱信号的进一步定量检测是基于混沌系统的两个特性，即对噪声的抗扰性和对微弱信号的敏感性而建立的。仿真实验表明，在保证精度的情况下，随着检测幅度的增大，抗噪声能力会增强。
We proposed a quantitative detection method for weak periodic signal in this paper. A result is obtained when analyzing the stable output of chaotic oscillator system in the large-scale periodic state, which shows that the average area of the periodic solution of the chaotic oscillator system is a steady geometric characteristic quantity of periodic solutions of the chaotic oscillator system. There is a steadily and monotonically increasing relation between the average area and the amplitude to be detected. When some parameters are defined, the precision of the geometric characteristic quantity can reach 10 -6 V 2 . The further quantitative detection of weak signals is built based on the two characteristics of the chaos system, namely the immunity to noise and sensitivity to weak signal. The simulation experiments shown that the immunity to noise will be enhanced along with the increase of amplitude detected while the precision can be guaranteed.