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 Study on Conjugate Quadrature Filters | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2011 Article ID 231754 7 pages doi 2011 231754 Research Article A Study on Conjugate Quadrature Filters Jin-Song Leng Ting-Zhu Huang Yan-Fei Jing and Wei Jiang School of Mathematical Sciences University of Electronic of Science and Technology of China Chengdu Sichuan 610054 China Correspondence should be addressed to Jin-Song Leng l-js2004@ Received 18 June 2010 Revised 26 October 2010 Accepted 5 January 2011 Academic Editor Antonio Napolitano Copyright 2011 Jin-Song Leng et al. 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. It is very important for generating an orthonormal multiwavelet system to construct a conjugate quadrature filter CQF . In this paper a general method of constructing a length- 1 CQF with multiplicity r and scale a from a length- CQF is obtained. As a special case we study generally the construction of a length- 1 CQF with multiplicity 2 and scale 2 which can generate a compactly supported symmetric-antisymmetric orthonormal multiwavelet system from a length- CQF. 1. Introduction and Preliminaries Wavelet analysis has been proven to be a very powerful tool in harmonic analysis neural networks numerical analysis and signal processing especially in the area of image compression 1 . Symmetry is a crucial property in signal processing. It is well known that the scalar orthonormal wavelet bases with compact support have no symmetry. Multiwavelets initiated by Goodman et al. 2 overcome the drawback. In practice orthonormal multiwavelets are of interest because they can be real compactly supported continuous and symmetric. The advantages of multiwavelets and their promising features in applications have attracted a great deal of interest and effort to extensively study them. For example the
