Constructions and algorithms of compactly supported biorthogonal multiwavelets and wavelet packets with scale 3
Luo Li-suo · Journal of Shaanxi Normal University · 2011
Constructions and algorithms of compactly supported biorthogonal multiwavelets and wavelet packets with scale 3 are discussed.The notion of multiresolution analysis(MRA) and the concept of biorthogonal multiwavelets are introduced.The scaling functions with a long support and r multiplicity can be transfered as the ones with a short support and r multiplicity.Two-scale matrix symbols are written as the forms of matrices through using the matrix theory,then the matrices are extended as the orthogonal ones and the equations about the two-scale matrix symbols are obtained.Two-scale matrix sequence of biorthogonal multiwavelets with scale 3 are given by solving the equations.The method can be used for any biorthogonal wavelets with compact support and with scale 3.The biorthogonal wavelet packets with multiplicity r and scale 3 are constructed by truncating a 2r-dimensionalvector-valued function to two r-dimensional vector-valued functions,baced on the theory of matrix and MRA.The equations about the coefficient matrices are obtained and the corresponding decomposition relations of coefficient matrices are presented.At last,biorthogonal properties of biorthogonal wavelet packets with scale 3 are investigated,which are the basis for constructing the wavelet basis for L2(R).