基于短时傅里叶变换的Duffing振子微弱信号检测

研究了Duffing振子信号检测过程中混沌、间歇混沌和大周期状态的时频特征,提出了一种基于检测统计量的任意频率信号检测方法。通过对系统不同状态下的输出序列进行短时傅里叶变换(STFT)发现,等幅线和三维时频分布能够体现出不同状态的显著差异,且可以完全区分出每一种状态。从构造统计量的易实现性出发,用三维时频分布中的幅时曲线作为衡量不同状态的依据,并将不同频率对应的幅时曲线的均值最大量作为检测统计量,该统计量的计算可以借助快速傅里叶变换(FFT)操作提高时效性。在此基础上,引入频率控制单元,给出了任意频率信号的检测方法步骤,方法的关键是将检测统计量最大值处所在的频率作为待测信号频率范围的一个端点,另一个端点为毗邻的两个检测统计量值较大者所在频率点。实验给出了不同状态的检测统计量范围,进而以此范围为判据,实现了振子对任意频率信号的检测,说明了方法的可行性,为Duffing振子信号检测问题的研究提供了一种新的思路。

Weak signal detection with Duffing oscillator based on short time Fourier transform

Time frequency characteristic of three statuses such as chaos, intermittent chaos and great period appearing in signal detection process with Duffing oscillator is studied and a frequency signal detection method based on new detection statistics is proposed. By analyzing on system output sequence in different statuses with short time Fourier transform (STFT), it is found that contour line of amplitude and three-dimensional time frequency distribution could represent differences of three statuses and recognize the three statuses utterly. Considering being easily operated on the detection statistics, amplitude-time characteristic in three-dimensional time frequency distribution is made as a foundation to weigh different statuses. Further, maximum of average value of number in amplitude-time characteristic corresponding to each frequency is set to final detection statistic, whose computation could be realized by fast Fourier transform (FFT) so that there will be high time effectiveness. On the basis of it, frequency control unit is brought in Duffing oscillator and scheme of any frequency signal detection is given. The key point of the scheme is to find the maximum among all detection statistics and makes its matching frequency as one port of unknown signal frequency range. Then the other port is the matching frequency of secondary maximum among other two detection statistics adjacent to the maximum. After experiment, the range of detection statistics of each status is given. Thus, according to the range, any frequency signal detection by Duffing oscillator is realized, which shows feasibility of the method and provides one new thought for studying signal detection problem with Duffing oscillator.