Parameterization of m-channel orthogonal multifilter banks

Abstract

A complete parameterization for the m-channel FIR orthogonal multifilter banks is provided based on the lattice structure of the paraunitary systems. Two forms of complete factorization of the m-channel FIR orthogonal multifilter banks for symmetric/antisymmetric scaling functions and multiwavelets with the same symmetric center 1/2(1 + γ + γ/(m - 1)) for some nonnegative integer γ are obtained. For the case of multiplicity 2 and dilation factor m = 2, the result of the factorization shows that if the scaling function φ and multiwavelet ψ are symmetric/antisymmetric about the same symmetric center γ + 1/2 for some nonnegative integer γ, then one of the components of φ (respectively ψ) is symmetric and the other is antisymmetric. Two examples of the construction of symmetric/antisymmetric orthogonal multiwavelets of multiplicity 3 with dilation factor 2 and multiplicity 2 with dilation factor 3 are presented to demonstrate the use of these parameterizations of orthogonal multifilter banks. © J.C. Baltzer AG, Science Publishers.