Theory Of The Generalized Daubechies Wavelet And Construction Of The Filter

Wavelet analysis in signal processing and image processing has a lot of applications. The thesis is an expansion of the wavelet analysis for the signal of type of trigonometric function.This thesis first introduced the development of wavelet theory and wavelet transform principle, focuses on the Daubechies wavelet function and the principle of the generalized Daubechies wavelet. It stresses the importance of the generalized Daubechies's three major characteristics which is compactly supported wavelets, orthogonality, and the index polynomial vanishing moment . Then it discuss the structure and application of the generalized Daubechies wavelet filter.The generalized Daubechies wavelet corresponds to the non-stationary multi-resolution analysis of the filter structure is dependent on the signal. In the thesis,according to the different natures of the generalized Daubechies wavelet and the classic Daubechies wavelet, we take the signal of type of trigonometric function based on the non-stationary multi-resolution analysis as an example, we achieve the construction of the generalized Daubechies wavelet filter firstly, then process the signal with the constructed filter. Then we process the signal with the classic Daubechies wavelet and compare the two results.The simulation result shows that the structure of the generalized Daubechies wavelet in the low-frequency filter can approximate the trigonometric functions very well, while the details of its component index has polynomial vanishing moments. These good natures have laid application basement of the generalized Daubechies wavelet.