The Characteristics Concerning a class of Orthogonal Multivariate Matrix-valued Scaling Functions and Frame Packets

Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. In this work, the notion of matrix-valued multiresolution analysis of space L-2(R-n,C-sxs) is introduced. A method for constructing orthogonal matrix-valued ternary wavelet packs is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are provided. Finally, new orthonormal wavelet pack bases of space L-2(R-n,C-sxs) are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.