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TitleSymmetric orthogonal filters and wavelets with linear-phase moments
Author(s) Bernard Hanzon
TypeArticle in Journal
AbstractIn this paper we study symmetric orthogonal filters with linear-phase moments, which are of interest in wavelet analysis and its applications. We investigate relations and connections among the linear-phase moments, sum rules, and symmetry of an orthogonal filter. As one of the results, we show that if a real-valued orthogonal filter a is symmetric about a point, then a has sum rules of order m if and only if it has linear-phase moments of order 2 m . These connections among the linear-phase moments, sum rules, and symmetry help us to reduce the computational complexity of constructing symmetric real-valued orthogonal filters, and to understand better symmetric complex-valued orthogonal filters with linear-phase moments. To illustrate the results in the paper, we provide many examples of univariate symmetric orthogonal filters with linear-phase moments. In particular, we obtain an example of symmetric real-valued 4-orthogonal filters whose associated orthogonal 4-refinable function lies in C 2 ( R ) .
KeywordsOrthogonal filters, Linear-phase moments, Symmetry, Sum rules, Complex orthogonal wavelets
ISSN0377-0427
URL http://www.sciencedirect.com/science/article/pii/S0377042711003311
LanguageEnglish
JournalJournal of Computational and Applied Mathematics
Volume236
Number4
Pages482 - 503
Year2011
NoteInternational Workshop on Multivariate Approximation and Interpolation with Applications (MAIA 2010)
Edition0
Translation No
Refereed No
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