利用Duffing方程组检测随机相位的正弦信号

摘要

We adopt an equation group of 16 equations to measure the weak sine signal with unknown phase place.The threshold values of the 16 equations are already confirmed.When the weak signal joins the system,we verify 16 equations one by one to see whether the phase portrait changes from chaos to big yardstick cycles in the systematic output.If so,this equation can be used to measure the signal.If not,the experiment is continued.We can find one or many equations that are suited finally.In this paper,we consider the mean of those equations with phase portrait changes as the amplitude of the weak signal%讨论用16个能产生混沌现象的方程来检测带有未知相位的微弱正弦信号。16个相位已经确定的方程的阈值事先求解出来。当未知相位的信号通过系统时,逐个验证方程,看是否有混沌向大尺度周期运动转变的方程,如果有,则此方程可以作为检测信号的方程,若没有则继续实验,最后必然会出现一个甚至多个相轨迹转变的方程。用能够出现相轨迹转变的方程检测到的信号平均值作为测得的微弱信号幅值