Matrix Transformations and Paraunitary Filter Banks
ABSTRACT This paper contains a discussion of the applications of matrix theory to filter bank construction. Firstly, two matrix transformations as well as their properties are examined. Secondly, the above results are applied to construct paraunitary filter banks, and the structures of those kinds of filters are studied. In the end, examples are developed to illustrate the proposed technique.
- SourceAvailable from: Carl R de Boor[show abstract] [hide abstract]
ABSTRACT: A second look at the authors' [BDR1], [BDR2] characterization of the approximation order of a Finitely generated Shift-Invariant (FSI) subspace of L 2(R d ) results in a more explicit formulation entirely in terms of the (Fourier transform of the) generators of the subspace. Further, when the generators satisfy a certain technical condition, then, under the mild assumption that the set of 1-periodizations of the generators is linearly independent, such a space is shown to provide approximation order k if and only if contains a (necessarily unique) satisfying for |j|<k , . The technical condition is satisfied, e.g., when the generators are at infinity for some >k+d. In the case of compactly supported generators, this recovers an earlier result of Jia [J1], [J2].Constructive Approximation 01/1998; 14(4):631-652. · 1.07 Impact Factor
- SIAM J. Matrix Analysis Applications. 01/2003; 25:517-531.
- [show abstract] [hide abstract]
ABSTRACT: this paper, we determine the accuracy p from the matrices c k . Moreover, we determine explicitly the coefficients y ff;i (k) such that x01/1999;