一种利用混沌测量低频频率的新方法

非线性Duffing方程在从混沌状态到大周期转变时，表现出良好的等Q共振锁频特性。本文研究了在不同谐振频率下，系统从混沌状态到大周期状态时驱动力信号的幅值及频率条件，指出不同的驱动力幅值，存在着相应的锁频范围。当驱动力幅值大于阈值的余度越大，则相应的锁频范围越宽。进而通过虚拟仪器的实现方式，将被测信号的幅值做不同程度的归一化，利用混沌阵列进行了精密测量频率。实验测试表明，该方法可达到较高的精度，不足之处在于由于计算机要完成不同程度的归一化，同时需要人工判别相图是处于混沌还是大周期状态，所以需要测试时间较长。由此可知该方法特别适合于低频、单次信号的高精度测频。

A New Method for Frequency Detection Based on Chaos

Nonlinear duffing equation expresses better equivalent Q resonant frequency locking property when system transits from chaotic to great periodic motion. The relation between amplitude and frequency of driven force is researched when the system transforms from chaotic state to great periodic state under different resonant frequencies. Result shows that the bigger of the amplitude of driven force, the wider of range of frequency locking. The amplitude of the detected signal is regulated to different degrees using virtual instrument and high precision frequency is detected by using chaos array. Experiment indicates that there are advantage in achieving higher precision and disadvantage in long test time because of regulation to different degrees by computer and determinant of system state from phase digram by mankind. So the method is in particular switable for high precision frequency detection for signals with low frequencies and single signals.