Journal Article10.1137/S0895479802412735
Multivariate Filter Banks Having Matrix Factorizations
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TL;DR: These filter banks are suitable for the construction of multivariate multiwavelets with a general dilation matrix built by a matrix factorization and it is shown that block central symmetric orthogonal matrices provide filter banks having a uniform linear phase.
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Abstract: In this paper 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.
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Citations
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References
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TL;DR: Among the topics discussed are sampling in multiple dimensions, multidimensional perfect reconstruction filter banks, the two-channel case in several dimensions, the synthesis of multiddimensional filter Banks, and the design of compactly supported wavelets.
Filter banks allowing perfect reconstruction
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Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters
TL;DR: Two perfect-reconstruction structures for the two-channel quadrature mirror filter bank, free of aliasing and distortions of any kind, in which the analysis filters have linear phase, are described in this article.
Using the Matrix Refinement Equation for the Construction of Wavelets on Invariant Sets
Charles A. Micchelli,Yuesheng Xu +1 more
TL;DR: In this article, the authors construct discontinuous wavelets on invariant sets in R n by using the matrix refinement equation and the basic operation of translation and scale, and show how to modify their construction to obtain continuous wavelets.
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Using the refinement equation for the construction of pre-wavelets V: extensibility of trigonometric polynomials
TL;DR: This paper provides a method using Householder transformations to construct matrices of trigonometric series which leads to multivariate wavelet decompositions.