基于变矩阵结构奇异值分解的信号分解算法

矩阵结构对奇异值分解的信号处理效果有重要影响,改变传统算法中矩阵结构固定的思想,提出在奇异值分解中采用变化的矩阵结构,每分解一次,矩阵结构就改变一次,以适应信号中不同的周期性分量。每次的分解都将上一层的信号分解为主、副两个分量,提取副分量,而对主分量再次进行变矩阵结构的奇异值分解,如此反复进行,最终将原始信号分解为一系列主、副分量。信号处理实例表明,这一方法具有良好的信号分离效果,能够实现信号中不同周期性分量的有效分离。

Signal Decomposition Algorithm Based on Varying Matrix Structure Singular Value Decomposition

The matrix structure has an important influence on the signal processing effect of the singular value decomposition (SVD), and the idea in traditional algorithm that matrix structure should be fixed is not adopted, while the varying matrix structure is proposed to be used in SVD. For every SVD, the matrix structure is changed once to adapt the different periodical components of the original signal, and then in every decomposition the signal of the previous layer is decomposed into the principal component and secondary component. The secondary component is retained, while the principal component is decomposed by the varying matrix structure SVD again, so repeatedly. Finally the original signal is decomposed into a series of principal and secondary components. The signal processing examples show that this method has a good separation effect on the different periodical components in the original signal.