Abstract: 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.