The Optimality Characters of Vector-Valued Binary Small-Wave Wraps with a Constant Dilation Factor
Frame theory has been the focus of active research for twenty years, both in theory and applications. In this work, the notion of orthogonal vector-valued binary small-wave wraps, which is a generalization of uni-wavelet packets, is introduced. A procedure for constructing them is presented. Their orthogonality traits are investigated by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas concerning these binary small-wave wraps are established. Orthonormal wavelet packet bases are obtained. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided.
M. P. Guo "The Optimality Characters of Vector-Valued Binary Small-Wave Wraps with a Constant Dilation Factor", Applied Mechanics and Materials, Vols. 58-60, pp. 1460-1465, 2011