05974057

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05974057 Li, Yonggan The characteristics of multiple affine oblique binary frames of translates with binary filter banks. Lin, Song (ed.) et al., Advances in computer science, environment, ecoinformatics, and education. International conference, CSEE 2011, Wuhan, China, August 21--22, 2011. Proceedings, Part I. Berlin: Springer (ISBN 978-3-642-23320-3/pbk; 978-3-642-23321-0/ebook). Communications in Computer and Information Science 214, 36-41 (2011). 2011 Berlin: Springer EN affine pseudoframes bivariate wavelet wraps wavelet frame Bessel sequence orthonormal bases time-frequency analysis approach

doi:10.1007/978-3-642-23321-0_6

Summary: Frame theory has been the focus of active research for twenty years, both in theory and applications. In this paper, the notion of a bivariate generalized multiresolution structure (BGMS) of the subspace $L^{2}(\Bbb R^{2})$, which is the generalization of frame multiresolution analysis, is proposed. The biorthogonanality traits on wavelet wraps are researched by using time-frequency analysis approach and variable separation approach. The construction of a BGMS of the Paley-Wiener subspace of $L^{2}(\Bbb R^{2})$ is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A procedure for designing a class of orthogonal vector-valued finitely supported wavelet functions is proposed by virtue of filter bank theory and matrix theory.