The Characteristics of Multiple Affine Oblique Binary Frames of Translates with Binary Filter Banks

Frame theory has been the focus of active research for twenty years, both in theory and applications. In this paper, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace 2 2 ( ) L R , 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 Paley-Wiener subspace of 2 2 ( ) L R 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 vectorvalued finitely supported wavelet functions is proposed by virtue of filter bank theory and matrix theory.