Theoretically, multiwavelets hold significant advantages over standard wavelets, particularly for solving more complicated problems, and hence are of great interest. It is pointed out in this paper that we must avoid those "multi-wavelets" being just pairs of standard wavelets. The main purpose of this paper is to charaterize a class of matrices which is crucial for the construction of orthogonal multi-wavelets with uniform linear phase.
[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
) 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].
[Show abstract][Hide abstract] ABSTRACT: We design vector-valued multivariate filter banks with a polyphase matrix built by a matrix factorization. These filter banks are suitable for the construction of multivariate multiwavelets with a general dilation matrix. We show that block central symmetric orthogonal matrices provide filter banks having a uniform linear phase. Several examples are included to illustrate our construction.
SIAM Journal on Matrix Analysis and Applications 01/2003; 25(2):517-531. DOI:10.1137/S0895479802412735 · 1.59 Impact Factor
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