Symmetric paraunitary matrix extension and parametrization of symmetric orthogonal multifilter banks

This paper is devoted to a study of symmetric paraunitary matrix extensions . The problem for a given compactly supported orthonormal scaling vector wi th some symmetric property, to construct a corresponding multiwavelet which also has the symmetric property, is equivalent to the symmetric paraunitar y extension of a given matrix. In this paper we study symmetric paraunitary extensions of two types of matrices which correspond to two different case s for the symmetry of the scaling vector: the components of the scaling vec tor hav or don't hav the same symmetric center. In this paper we also discu ss parametrizations of symmetric orthogonal multifilter banks.