• CN：11-2187/TH
• ISSN：0577-6686

• 仪器科学与技术 •

### 奇异值分解对连续Morlet小波变换的压缩和提纯

1. 华南理工大学机械与汽车工程学院 广州 510640
• 出版日期:2015-08-20 发布日期:2015-08-20
• 基金资助:
国家自然科学基金(51375178)和广东省自然科学基金(S2012010008789)资助项目

### Purification and Compression of Continuous Morlet Wavelet Transform Based on Singular Value Decomposition

ZHAO Xuezhi, CHEN Tongjian, YE Bangyan

1. School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640
• Online:2015-08-20 Published:2015-08-20

Abstract: The linear correlation of row vectors of the continuous Morlet wavelet transform matrix is studied, this correlation make the result of continuous Morlet wavelet transform be of great redundancy, and singular value decomposition(SVD) is proposed to compress this redundancy. Theoretical analysis shows that the continuous Morlet wavelet transform matrix can be compressed into a few non-zero singular values and the corresponding orthogonal singular vectors by SVD technology. The ratio of the data size before and after compression is analyzed, and it is shown that the larger the matrix dimension, the better the compression effect. The distribution characteristics of singular values of the continuous Morlet wavelet transform results of the deterministic signal and the noise is studied, and it is found that the number of the effective singular values of the deterministic signal is determined by the number of frequencies in this signal, and the other singular values after the effective ones will soon drop to zero, while the singular values of noise is changed evenly and its falling speed is slow. This difference between the singular values of the deterministic signal and the noise is utilized, the purification of the continuous Morlet wavelet transform result of noisy signal can be realized, if the appropriate front singular values are chosen for SVD reconstruction, then the information of most noise singular values is discarded, thus the influence of noise on continuous Morlet wavelet transform is erased to a great extent.