Basis function analysis in Daubechies wavelet transformation
Description
This dissertation presents the research for the basis function analysis in the Daubechies wavelet transform. The goal of this research is to analyze the characteristics of the basis function and generate a new orthonormal bases set to attenuate the frequency responses of the cascaded filter banks without the regularity and the vanish conditions. A new parameter is introduced into the response polynomial to move the zero pair of 4-tap filter on unit circle and to control the behaviors of the cascaded filter banks. The new scaling coefficients are derived and solved by using the orthonormal conditions Moreover, this new parameter allows the new orthonormal basis to improve the octave frequency spacing of subband filters. The optimal value of new parameter is determined by using the minimax optimization to minimize the sidelobes of the cascaded filter banks. The sensitivity of the new parameter is investigated as well. The scaling coefficients for the optimal value are used to perform several thresholding schemes and uniform quantization. A best tree structure based on the minimum entropy criterion for the optimal value of the new parameter is presented to analyze signals. The optimal value of the new parameter is presented to analyze signals. The optimal value of wavelet packets are applied to describe the performance and compared with the standard Daubechies wavelets The comparison of the Daubechies wavelets and the new scaling coefficients is made by using scalogram and energy distribution to show components of signals which are localized in both domains. The achievement of the new scaling coefficients give more freedom and better attenuation to control the behaviors of the subband filters