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On the splitting trick and wavelets packets with arbitrary dilation matrix of L2(Rs)

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  • Han, Jincang
  • Cheng, Zhengxing

Abstract

Wavelet packets possess excellent characteristics in differentiations of space and spectrum. In this paper, The splitting trick coined by Daubechies is used to construct wavelet packets with an arbitrary dilation matrix A. Different from the classical wavelet packets, instructed by Coifman et al., our method is that we split the wavelet subspaces directly instead of using the low-pass and the high-pass filters associated with the multiresolution analysis. Furthermore, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation matrix not equal to 2I. Finally, we show how to construct various Riesz basis from the wavelet packets.

Suggested Citation

  • Han, Jincang & Cheng, Zhengxing, 2009. "On the splitting trick and wavelets packets with arbitrary dilation matrix of L2(Rs)," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 130-137.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:130-137
    DOI: 10.1016/j.chaos.2007.07.026
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    References listed on IDEAS

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    1. El Naschie, M.S., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
    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. 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.
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