Journal of Applied Mathematics
Volume 2012 (2012), Article ID 907175, 20 pages
http://dx.doi.org/10.1155/2012/907175
Research Article

Symmetry Feature and Construction for the 3-Band Tight Framelets with Prescribed Properties

Jianjun Sun,1 Bin Huang,2 Xiaodong Chen,2 and Lihong Cui2

1College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China
2School of Science, Beijing University of Chemical Technology, Beijing 100029, China

Received 5 July 2012; Accepted 29 August 2012

Academic Editor: Jingxin Zhang

Copyright © 2012 Jianjun Sun 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.

Abstract

A construction approach for the 3-band tight wavelet frames by factorization of paraunitary matrix is developed. Several necessary constraints on the filter lengths and symmetric features of wavelet frames are investigated starting at the constructed paraunitary matrix. The matrix is a symmetric extension of the polyphase matrix corresponding to 3-band tight wavelet frames. Further, the parameterizations of 3-band tight wavelet frames with filter lengths are established. Examples of framelets with symmetry/antisymmetry and Sobolev exponent are computed by appropriately choosing the parameters in the scheme.