Daubechies小波系数新解法

A novel solution for wavelet coefficients of Daubechies

小波分析是当前信号处理的的热门方向,涉及多个专业领域。经典小波理论深奥难懂,超出了一般高等数学的范畴,文中以Daubechies小波为例,对经典小波理论的推导以通俗方式进行了简化,为了便于读者的理解,给出详细的推导过程,并引用小波矩阵来表达。对采样序列数据进行小波分解和重构,经过小波重构可准确无损地恢复到原始数据。把小波正交性对应着小波矩阵的正交性,多次的双尺度分解,就可得到多分辩率的结果。文中给出了双尺度小波分解在故障异常、励磁涌流、开关函数波形分析的工程案例,并提出了边缘失真问题的有效解决办法。

Wavelet analysis is a popular direction of signal processing,which involves many specialized fields.The classical wavelet theory is abstruse and hard to understand,it is beyond the scope of general higher mathematics,this paper takes Daubechies wavelet as an example,the derivation of classical wavelet theory is simplified generally,for the sake of easy understanding of the readers,the derivation process is detailed,and finally it is introduced to express with wavelet matrix.The sampling sequence data can be decomposed and reconstructed by wavelet,and the original data can be recovered accurately and nondestructively by wavelet reconstruction.If the orthogonality of wavelet corresponds to the orthogonality of wavelet matrix,the result of multiresolution can be obtained by multiple biscale decomposition.Finally,this paper presents the engineering cases of the analysis of the waveforms of the double-scale wavelet decomposition in fault anomaly,excitation insurge current and switch function,and puts forward the effective solutions to the problem of edge distortion.