Parameterization of m‐channel orthogonal multifilter banks

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\frac{1}{2}$$ \end{document} (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 + \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\frac{1}{2}$$ \end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\frac{1}{2}$$ \end{document} 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.