基于奇异值分解和Savitzky-Golay滤波器的信号降噪方法

为降低信号中噪声的干扰,将奇异值分解(SVD)理论和Savitzky-Golay滤波器相结合提出了一种新的降噪方法。该方法首先分析了信号负熵随信噪比变化的规律,而后通过将负熵作为降噪效果的评估参数,确定了SVD降噪过程中构造的Hankel矩阵的最优维数;其次采用Savitzky-Golay滤波器对用于重构信号的奇异值进行了平滑滤波处理,并分析了Savitzky-Golay滤波器结构对降噪效果的影响,最后通过定义误差函数确定了Savitzky-Golay滤波器的最优结构。将该方法应用于线性调频信号和多成分周期信号的降噪实验,结果表明:基于SVD和Savitzky-Golay滤波器的降噪方法能有效降低噪声干扰,是一种有效的信号降噪方法。

Signal denoising method based on singular value decomposition and Savitzky-Golay filter

In order to reduce the noise of signal, a new denoising approach was proposed based on Singular Value Decomposition (SVD) and Savitzky-Golay filter. The change law of negentropy with Signal-to-Noise Ratio (SNR) was analyzed, then the negentropy was treated as an evaluating parameter of noise suppression, and the optimal dimension of the Hankel matrix of the signal was obtained. Then the Savitzky-Golay filter was used to process the singular values which are used to reconstruct the denoised signal, and the effect of Savitzky-Golay filter configuration on denoising result was studied, then the optimal configuration of Savitzky-Golay filter was determined by defining error function. The proposed approach was applied to multi-component periodic signal and linear frequency modulation signal denoising. The result shows that the proposed approach can reduce the noise effectively, and it is an effective denoising approach.