Symmetric-antisymmetric orthonormal multiwavelets and related scalar wavelets

For compactly supported symmetric-antisymmetric orthonormal multiwavelet sy stems with multiplicity 2, we first show that any length-2N multiwavelet sy stem can be constructed from a length-(2N + 1) multiwavelet system and vice versa. Then we present two explicit formulations for the construction of m ultiwavelet functions directly from their associated multiscaling functions . This is followed by the relationship between these multiscaling functions and the scaling functions of related orthonormal scalar wavelets. Finally, we present two methods for constructing families of symmetric-antisymmetri c orthonormal multiwavelet systems via the construction of the related scal ar wavelets. (C) 2000 Academic Press.