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

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  • Huang, Yongdong
  • Cheng, Zhengxing

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.

Suggested Citation

  • Huang, Yongdong & Cheng, Zhengxing, 2007. "Minimum-energy frames associated with refinable function of arbitrary integer dilation factor," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 503-515.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:503-515
    DOI: 10.1016/j.chaos.2006.06.082
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    1. El Naschie, M.S., 2006. "Hilbert space, the number of Higgs particles and the quantum two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 9-13.
    2. El Naschie, M.S., 2005. "A guide to the mathematics of E-infinity Cantorian spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 955-964.
    3. Svozil, Karl, 2005. "Computational universes," Chaos, Solitons & Fractals, Elsevier, vol. 25(4), pages 845-859.
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    Cited by:

    1. Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Construction and characterizations of orthogonal vector-valued multivariate wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1835-1844.

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