关键词: 奇异值分解, 矩阵构造, 正交, 信号处理, 特征提取

Abstract:

Generally, two kinds of matrices can be created by a one-dimension signal. The first one is always created by the continuous interception of signal, while the second one is a reconstruction attractor matrix. It is proved that a signal can be decomposed into the linear superposition of a series of component signals by singular value decomposition （SVD） using these two kinds of matrices. However, the component signals obtained by the first kind of matrix are orthogonal with each other, while those obtained by the second one are correlative with each other. The structure of both kinds of matrices can be rationally determined by the variation trend of information quantity of component signals. The processing results of a milling force signal show that, by using the first kind of matrix, the complete fundamental waveform of main spindle of miller is isolated, two component signals with close frequency are distinguished, and the phenomenon of amplitude modulation hidden in signal is also extracted; while by using the second one, the faint shock to cutter due to the uneven granule and rift in workpiece material is revealed.

Key words: singular value decomposition, matrix creation, orthogonality, signal processing, feature extraction