Minimum-energy frames associated with refinable function of arbitrary integer dilation factor

Yongdong Huang and Zhengxing Cheng

Chaos, Solitons & Fractals, 2007, vol. 32, issue 2, 503-515

Abstract: In this paper, we study minimum-energy frame Ψ={ψ1,ψ2,…,ψN} with arbitrary integer dilation factor d for L2(R), Ψ correspond to some refinable functions with compact support. A precise existence criterion of Ψ is given in terms of an inequality condition on the Laurent polynomial symbols of the refinable functions. We give a constructive proof that when Ψ does exist, d functions with compact support are sufficient to constitute Ψ, and present a explicit formula of constructing Ψ. Finally, we present the minimum-energy frames decomposition and reconstruction formulas which are similar to those of orthogonal wavelets. Numerical examples are given.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:32:y:2007:i:2:p:503-515

DOI: 10.1016/j.chaos.2006.06.082

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