The Research of the Orthogonality Property of Matrix Univariate Wavelet Packets with an Integer Dilation Factor
Shude Du, Hong-E Wu · 2009
The notion of matrix-valued multiresolution analysis. A procedure for designing orthogonal matrix-valued univariate wavelet packets is presented and their orthogonality properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal basis of L2(R, Cu × u) are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.