基于奇异值分解和Savitzky-Golay滤波器的信号降噪方法

doi:10.11772/j.issn.1001-9081.2015.10.3004

计算机应用 ›› 2015, Vol. 35 ›› Issue (10): 3004-3007.DOI: 10.11772/j.issn.1001-9081.2015.10.3004

基于奇异值分解和Savitzky-Golay滤波器的信号降噪方法

朱红运, 王长龙, 王建斌, 马晓琳

军械工程学院无人机工程系, 石家庄 050003

收稿日期:2015-05-08 修回日期:2015-07-08 出版日期:2015-10-10 发布日期:2015-10-14
通讯作者: 王长龙(1965-),男,河北沧州人,教授,博士师导师,博士,主要研究方向:信号处理、智能信息处理,wang_oec@126.com
作者简介:朱红运(1988-),男,河南开封人,博士研究生,主要研究方向:信号处理;王建斌(1967-),男,河北保定人,副教授,主要研究方向:智能信息处理、无损检测;马晓琳(1979-),女,河北石家庄人,讲师,硕士,主要研究方向:信号处理。
基金资助:
"十二五"装备预先研究项目(51325010602);河北省自然科学基金资助项目(E2015506004)。

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

ZHU Hongyun, WANG Changlong, WANG Jianbin, MA Xiaolin

Department of Unmanned Aerial Vehicles Engineering, Ordnance Engineering College, Shijiazhuang Hebei 050003, China

Received:2015-05-08 Revised:2015-07-08 Online:2015-10-10 Published:2015-10-14

摘要/Abstract

摘要： 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。

关键词: 降噪, 奇异值分解, 负熵, Savitzky-Golay滤波器, Hankel矩阵

Abstract: 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.

Key words: denoising, Singular Value Decomposition (SVD), negentropy, Savitzky-Golay filter, Hankel matrix

中图分类号:

TN911.4

朱红运, 王长龙, 王建斌, 马晓琳. 基于奇异值分解和Savitzky-Golay滤波器的信号降噪方法[J]. 计算机应用, 2015, 35(10): 3004-3007.

ZHU Hongyun, WANG Changlong, WANG Jianbin, MA Xiaolin. Signal denoising method based on singular value decomposition and Savitzky-Golay filter[J]. Journal of Computer Applications, 2015, 35(10): 3004-3007.

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基于奇异值分解和Savitzky-Golay滤波器的信号降噪方法

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

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