利用奇异值分解的信号降噪方法
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    摘要:

    为了提高测试信号的信噪比,针对奇异值分解降噪法中有效秩阶次的选择以及重构矩阵 结构的确定两个关键问题,提出了一种基于信号频率成分的奇异值降噪方法。该方法利用信 号快速傅里叶变换结果中主频率个数来确定有效秩阶次,通过降噪信号的信噪比和均方差大 小确定重构矩阵结构,并采用不同频率成分的几组信号对该方法进行了验证。结果表明, 有效秩的阶次是源信号主频个数的2倍,并且这种倍数关系不随重构矩阵行列数的变化而变化 ;在工程应用中,重构矩阵的最佳行数取信号数据长度的一半,可以得到较好的降噪效果;除傅 里叶变换结果中有用信号频率与噪声频率难以区分的情形外,无论是白噪声还是色噪声,该方 法都十分有效。

    Abstract:

    The order of effective rank and the row number of reconstruction matrix both are difficult to determine for noise reduction based on singular value de composition. In order to increase the signal to noise ratio of test signals, a new effective method is presented to solve this problem. According to the relati onship between signal frequency and the distribution of singular value, the order of effective rank is determined by the number of dominating frequency in the fast flourier translation result of the signal and the optimal row number of rec onstruction matrix is determined by the signal to noise ratio (SNR) and the mea n square error (MSE) of the denoised signal. A numerical simulation using differ ent signals with different frequency components is employed. The results show that the order of the effective rank is twice as the number of dominating freq uency and it does not change with the variation of the row number. The optimal r o w number can be defined as half the length of the signal in engineering applic ation. This method both has good noise reduction accuracy and stability with whi te noise and colored noise when the dominating frequency can be distinguished in the power spectrum.

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