Parameterization of m band affine frames with pre-assigned scaling filter

Authors:
Zeyin Zhang;Daren Huang
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou, China;Department of Mathematics, ZhongShan University, GuangZhou, China
Venue:
Journal of Computational and Applied Mathematics - Special issue on proceedings of the international symposium on computational mathematics and applications
Year:
2004

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Abstract

Affine (wavelet) frames related with subdivision scheme provide tools for building curves and surfaces in CAGD/CAM. At first we show that scaling filters can be parameterized by decomposed elementary matrices with the form Im - P + Pz-k where k is a nonnegative integer, and P is a one rank constant-valued idempotent matrix P2 = Im (Theorem 2.2). Then we use the method to construct m band affine (wavelet) frames with the given scaling filter and the dual frames. General solutions for affine (wavelet) frames and its dual affine (wavelet) frames are obtained with pre-assigned scaling filter (Theorems 3.5 and 3.6). At last a design example is given.