变结构SVD算法及其在信号分离中的应用

发布时间：2018-06-03 06:27

本文选题：奇异值分解 + 变矩阵结构　；参考：《机械工程学报》2017年22期

【摘要】：利用奇异值分解(Singular value decomposition,SVD)进行信号处理的关键在于矩阵的构造,为利用SVD分离信号中的不同频率成分,提出一种变矩阵结构递推SVD算法,其思想是在SVD递推分解过程中逐次改变矩阵的结构,每进行一次SVD分解,矩阵的结构就规律性地变化一次,由此形成对信号中不同频率成分的适应性,从而达到将其分离出来的目的。推导出这种变结构SVD的信号分解算法,证明了这种算法可以将原始信号分解为一系列分量信号的线性组合。进一步从理论上分析了这种算法的信号分离机理,证明了对于一些特定的频率结构,这种变结构SVD算法可以实现对原信号中单个频率分量的逐次分离。最后通过对模拟信号和工程实际信号的分离实例证实了变结构SVD算法良好的信号分离效果,并与小波分析和多分辨SVD方法进行了比较,结果表明变结构SVD的信号分离结果优于这两种方法。
[Abstract]:The key of signal processing using singular value decomposition (SVD) is the construction of matrix. In order to separate different frequency components of signals by SVD, a recursive SVD algorithm with variable matrix structure is proposed. The idea is to change the structure of the matrix step by step in the process of SVD recursive decomposition. With each SVD factorization, the structure of the matrix changes regularly, thus forming the adaptability to the different frequency components of the signal. In order to achieve the purpose of separating it. The signal decomposition algorithm of the variable structure SVD is derived and it is proved that the algorithm can decompose the original signal into a series of linear combination of component signals. Furthermore, the signal separation mechanism of this algorithm is analyzed theoretically, and it is proved that the variable structure SVD algorithm can realize the successive separation of a single frequency component in the original signal for some specific frequency structures. Finally, the example of signal separation between analog signal and engineering signal proves that the variable structure SVD algorithm has good signal separation effect, and it is compared with wavelet analysis and multi-resolution SVD method. The results show that the signal separation results of variable structure SVD are better than those of these two methods.
【作者单位】：华南理工大学机械与汽车工程学院;
【基金】：国家自然科学基金(51375178) 广东省自然科学基金(S2012010008789)资助项目
【分类号】：TN911.7

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