Quaternion-valued Smooth Orthogonal Wavelets with Short Support and Symmetry

  • Lizhong Peng
  • Jiman Zhao
Part of the Trends in Mathematics book series (TM)


In this paper, we define the quaternion-valued multiresolution analysis of L 2 ℝ, H). We give the properties of the scaling functions, wavelet functions and their corresponding low-pass and high-pass filters, and present a sufficient condition for the existence of the quaternion-valued wavelet. By solving the system of equations, we obtain some kinds of low-pass filters and high-pass filters with short support and symmetry of smooth orthogonal wavelets. We also construct quaternion-valued wavelets of a quaternion variable on L 2 (H,H).


Quaternion-valued multiresolution analysis scaling function wavelet function low-pass filter high-pass filter. 


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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Lizhong Peng
    • 1
  • Jiman Zhao
    • 2
  1. 1.LMAM, School of Mathematical SciencesPeking UniversityBeijingP.R. China
  2. 2.MM Key Lab., Academy of Mathematics and System SciencesChinese Academy of SciencesBeijingP.R. China

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