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Construction and properties of orthogonal matrix-valued wavelets and wavelet packets

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  • Chen, Qingjiang
  • Shi, Zhi

Abstract

In this paper, we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets with arbitrary integer dilation factor m. A necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets is derived by virtue of paraunitary vector filter bank theory. An algorithm for constructing compactly supported m-scale orthogonal matrix-valued wavelets is presented. The notion of orthogonal matrix-valued wavelet packets is proposed. Their properties are investigated by means of time–frequency method, operator theory and matrix theory. In particular, it is shown how to construct various orthonormal bases of space L2(R,Cr×r) from these wavelet packets, and the orthogonal decomposition relation is also given.

Suggested Citation

  • Chen, Qingjiang & Shi, Zhi, 2008. "Construction and properties of orthogonal matrix-valued wavelets and wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 75-86.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:1:p:75-86
    DOI: 10.1016/j.chaos.2007.08.006
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    1. 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.
    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.
    4. Iovane, Gerardo & Giordano, Paola, 2007. "Wavelets and multiresolution analysis: Nature of ε(∞) Cantorian space–time," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 896-910.
    5. 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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    Cited by:

    1. Sun, Lei & Li, Gang, 2009. "Generalized orthogonal multiwavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2420-2424.

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