基于Duffing振子的微弱正弦信号检测方法研究

利用混沌振子系统的初值敏感性和对噪声的免疫力检测微弱正弦信号，可以获得很高的检测灵敏度和很好的抗噪性能。文中分析了待测正弦信号幅值和相位对混沌系统状态的影响。基于Duffing振子系统的相变特性，提出了检测微弱正弦信号幅值和相位的新方法，即：反相补偿幅值检测方法和三分对称相位检测方法，介绍了检测的原理和具体实现步骤；利用Duffing方程的位移X波形的包络特性，提出了适合于含噪声情况的混沌特性自动判别方法，以正确判别混沌系统的状态并应用于文中的信号检测方法之中。最后，将该方法和最大似然法进行了比较。数字仿真结果证明了文中所提方法的可行性和有效性。只需改变策动力的频率，该方法即可适用于检测各种频率的微弱正弦信号，对于扩大光传感器的测量范围、电力系统谐波分析等应用具有实用价值。

STUDY ON DETECTION OF WEAK SINUSOIDAL SIGNAL BY USING DUFFING OSCILLATOR

The chaotic system is sensitive to the initial conditions and immune to noise. Using the Duffing oscillator, detection of weak sinusoidal signal has good detection sensitivity and anti-interference capability. The effect of the amplitude and phase of a detected sinusoidal signal to the state of chaotic system was analyzed. Based on the motion transition of a chaotic oscillator, new methods to detect weak sinusoidal signal were brought forward, called reverse-phase-compen sation-amplitude-estirnation and trisection-symmetry-phase estimation. The detection principles and realization procedures were introduced. For the detection of signal with noise, by using the envelope characteristic of X-wave of Duffing equation, the method of identifying chaos nature automatically was presented to distinguish the chaotic system state correctly, and employed in the signal detection in this paper. At last, the signal detection methods were compared with the maximum likelihood method. The digital simulation results show that new methods are feasible and effective. By modifying the driving frequency, these methods are fit for detecting weak sinusoidal signal with any frequency, which are useful for expending measure range of the optical transducer and harmonic analysis of electric power system. By modifying the driving frequency, these methods are fit for detecting weak sinusoidal signal with any frequency, which are useful for expending measure range of the optical transducer and harmonic analysis of electric power system.