多分辨SVD包理论及其在信号处理中的应用

Multi-resolution SVD Packet Theory and Its Application to Signal Processing

在奇异值分解(singular value decomposition,SVD)中提出了一种矩阵递推构造和分解算法,利用SVD实现了一种类似于小波包的信号分解方式,称之为多分辨SVD包.推导了多分辨SVD包的分解和重构算法,并提出一种用二维数组来存储这种包的三维数据的方法,避免了对内存的浪费.实例结果表明,这种包对信号的微弱变化具有优良的检测能力,其检测结果无幅值和相位失真,并能精确定位微弱变化的位置,这种包也能有效提取复杂信号中的弱故障特征,在这两方面均明显优于小波包的处理结果.

The recursion creation and decomposition of matrix is introduced into singular value decomposition （SVD）, and a signal decomposition way, which is similar to wavelet packet and is called multi-resolution SVD packet, is realized with SVD. The decomposition and recomtruction algorithms of multi-resolution SVD packet are given. Besides, a method in which two dimonsional array is used to store the three-dimensional data of this packet is proposed so that the waste of computer memory can be avoided. The results of examples show that this packet has good ability to detect the faint change of signal, and the accurate position of faint change can be reliably detected, and furthermore,there is no distortion of amplitude and phase in detection result. In addition, this packet can effectively extract the weak fault feature from the complicated signal. In these two cases the processing results of multi resolution SVD packet is much better than those of wavelet packet.