Details:
Title  Symmetric orthogonal filters and wavelets with linearphase moments  Author(s)  Bernard Hanzon  Type  Article in Journal  Abstract  In this paper we study symmetric orthogonal filters with linearphase moments, which are of interest in wavelet analysis and its applications. We investigate relations and connections among the linearphase moments, sum rules, and symmetry of an orthogonal filter. As one of the results, we show that if a realvalued orthogonal filter a is symmetric about a point, then a has sum rules of order m if and only if it has linearphase moments of order 2 m . These connections among the linearphase moments, sum rules, and symmetry help us to reduce the computational complexity of constructing symmetric realvalued orthogonal filters, and to understand better symmetric complexvalued orthogonal filters with linearphase moments. To illustrate the results in the paper, we provide many examples of univariate symmetric orthogonal filters with linearphase moments. In particular, we obtain an example of symmetric realvalued 4orthogonal filters whose associated orthogonal 4refinable function lies in C 2 ( R ) .  Keywords  Orthogonal filters, Linearphase moments, Symmetry, Sum rules, Complex orthogonal wavelets  ISSN  03770427 
URL 
http://www.sciencedirect.com/science/article/pii/S0377042711003311 
Language  English  Journal  Journal of Computational and Applied Mathematics  Volume  236  Number  4  Pages  482  503  Year  2011  Note  International Workshop on Multivariate Approximation and Interpolation with Applications (MAIA 2010)  Edition  0  Translation 
No  Refereed 
No 
