Details:
Title | Symmetric orthogonal filters and wavelets with linear-phase moments | Author(s) | Bernard Hanzon | Type | Article in Journal | Abstract | In 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 ) . | Keywords | Orthogonal filters, Linear-phase moments, Symmetry, Sum rules, Complex orthogonal wavelets | ISSN | 0377-0427 |
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 |
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