Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A New Scheme for the Design of Hilbert Transform Pairs of Biorthogonal Wavelet Bases Hongli Shi and Shuqian Luo | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2010 Article ID712105 7 pages doi 2010 712105 Research Article A New Scheme for the Design of Hilbert Transform Pairs of Biorthogonal Wavelet Bases Hongli Shi and Shuqian Luo College of Biomedical Engineering Capital Medical University Beijing 100069 China Correspondence should be addressed to Hongli Shi shl@ Received 29 August 2010 Accepted 10 November 2010 Academic Editor Ulrich Heute Copyright 2010 H. Shi and S. Luo. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. In designing the Hilbert transform pairs of biorthogonal wavelet bases it has been shown that the requirements of the equalmagnitude responses and the half-sample phase offset on thelowpass filters are the necessary and sufficient condition. In this paper the relationship between the phase offset and the vanishing moment difference of biorthogonal scaling filters is derived which implies a simple way to choose the vanishing moments so that the phase response requirement can be satisfied structurally. The magnitude response requirement is approximately achieved by a constrained optimization procedure where the objective function and constraints are all expressed in terms of the auxiliary filters of scaling filters rather than the scaling filters directly. Generally the calculation burden in the design implementation will be less than that of the current schemes. The integral of magnitude response difference between the primal and dual scaling filters has been chosen as the objective function which expresses the magnitude response requirements in the whole frequency range. Two design examples illustrate that the biorthogonal wavelet bases designed by the proposed scheme are very close to Hilbert transform pairs. 1. Introduction The .
