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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.
MSC:
42C40Wavelets and other special systems
13B25Polynomials over commutative rings
94A11Application of orthogonal and other special functions in communication
15A23Factorization of matrices