小波奇异值分解的瞬变弱信号检测

Detection of transient weak signal based on wavelet transform and singular value decomposition

研究小波阈值法和奇异值分解法,分析最大分解层数、阈值函数、小波基函数的选取以及窗长和保留奇异值个数等参数的选择,并在此基础上提出小波与奇异值分解相结合降噪检测信号的方法。该方法首先将信号作小波分解,再对小波分解系数作奇异值分解,最后通过阈值法保留小波系数并重建降噪信号,利用重建信号进行信号检测。结果表明:该方法能更好地区分信号和噪声,获得更好的降噪和检测结果。

The wavelet-threshold method and the singular value decomposition （SVD） were introduced for detection of transient weak signal.Detailed aspects in the methods were discussed,including how to select the maximum decomposition level,threshold function,wavelet basis function,window length and the effective singular value number.A new detecting method integrating the wavelet method and the singular value decomposition was put forward.In the method,the transient weak signal is decomposed by db2 wavelet,and then the wavelet coefficients which are de-noised by singular value decomposition are used to reconstruct the signal.Simulation results demonstrate that the proposed method is efficient in distinguishing the transient weak signal from noise.By comparison,the proposed method outperforms the wavelet-threshold method and SVD.