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Symmetric paraunitary matrix extension and parametrization of symmetric orthogonal multifilter banks. (English) Zbl 0992.42022
Summary: This paper is devoted to a study of symmetric paraunitary matrix extensions. The problem to construct, for a given compactly supported orthonormal scaling vector with some symmetric property, a corresponding multiwavelet which also has the symmetry property, is equivalent to the symmetric paraunitary extension of a given matrix. In this paper we study symmetric paraunitary extensions of two types of matrices which correspond to two different cases for the symmetry of the scaling vector: the components of the scaling vector have or don’t have the same symmetric center. In this paper we also discuss parametrizations of symmetric orthogonal multifilter banks.
42C40Wavelets and other special systems
13B25Polynomials over commutative rings
94A11Application of orthogonal and other special functions in communication
15A23Factorization of matrices