基于稀疏分解的自适应数字锁定放大器微弱信号检测方法

A Weak Signal Detection Method of Adaptive Digital Lock-in Amplifier Based on Sparse Decomposition

提出了一种利用软件算法来自适应地实现数字锁定放大器的微弱正弦信号的检测,即利用稀疏分解的匹配追踪算法来实现这种检测方法.将稀疏分解中原子库的原子(即具有随机性的频率和初始相位的正弦波)作为参考信号,利用匹配追踪算法来搜索原子库(由多个原子组成)中的最优原子——即与输入有用信号最匹配相干的原子并可以得到该最优原子的幅度,由该最优原子的幅度、频率和初始相位信息就可以估计得到输入有用信号的对应参数,从而检测估计出输入信号中的有用正弦信号.该方法无需人工调节参考信号的幅度、频率和初始相位,只需修改算法中的某些参数即可实现微弱信号检测,在应用中就会更加方便、灵活.计算机模拟表明,可以精确地检测出带噪信号中有用的正弦信号和调幅AM信号,并且在-40 dB以下极低信噪比环境下还可以同时检测出多个被强噪声淹没的有用正弦信号.

The paper proposes a method which realizes adaptively weak sinusoidal signal detection of digital lock-in amplifier by software algorithm.The detection method is realized by matching pursuit（MP） algorithm of sparse decomposition.In the method,an atom of atoms of MP algorithm is a reference signal,and the atom is a sinusoidal wave which possesses random frequency and the initial phase,then it uses MP algorithm to search the optimal atom of atoms and obtains its amplitude,that is to say,the optimal atom is the atom of most matching correlation with a useful input signal,so it can estimate the corresponding parameters of the useful input signal through the messages of amplitude,frequency and the initial phase of the optimal atom and detect useful sinusoidal signal of the input one.With this method,it is not necessary to manually adjust the amplitude,frequency and the initial phase of the reference signal,and what is needed is only to modify some parameters of the algorithm to realize detection of weak signals.It is more convenient and flexible in the application.Computer simulation showed that this method can accurately detect useful sinusoidal signals and AM signals of the noise signals and it can detect multiple useful sinusoidal signals in a strong noise environment of the very low SNR of-40 dB.