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Construction and characterizations of orthogonal vector-valued multivariate wavelet packets

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  • Chen, Qingjiang
  • Cao, Huaixin
  • Shi, Zhi

Abstract

In this paper, the notion of orthogonal vector-valued wavelet packets of the space L2(Rs,Cd) is introduced. A method for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are investigated by virtue of time–frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas with respect to the wavelet packets are established. Orthogonal decomposition relation formulas of L2(Rs,Cd) are obtained by constructing a series of subspaces of vector-valued wavelet packets. In particular, it is shown how to construct various orthonormal bases of L2(Rs,Cd) from these wavelet packets.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:1835-1844
    DOI: 10.1016/j.chaos.2007.09.066
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    References listed on IDEAS

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    1. El Naschie, M.S., 2007. "Feigenbaum scenario for turbulence and Cantorian E-infinity theory of high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 911-915.
    2. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    3. 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.
    4. El Naschie, M.S., 2006. "Superstring theory: What it cannot do but E-infinity could," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 65-68.
    5. Naschie, M.S. El, 2006. "Fractal black holes and information," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 23-35.
    6. 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.
    7. Chen, Qingjiang & Cheng, Zhengxing, 2007. "A study on compactly supported orthogonal vector-valued wavelets and wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 1024-1034.
    8. 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.
    9. Svozil, Karl, 2005. "Computational universes," Chaos, Solitons & Fractals, Elsevier, vol. 25(4), pages 845-859.
    10. Chen, Qingjiang & Cheng, Zhengxing & Wang, Cuiling, 2007. "Affine pseudoframes for subspaces of L2(R) associated with a generalized multiresolution structure," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1401-1411.
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    Cited by:

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