Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ORTHOGONAL TWO-DIRECTION REFINABLE FUNCTION OF ORDER 3

  • KWON, SOON-GEOL (Department of Mathematics Education, Sunchon National University)
  • Received : 2019.02.28
  • Accepted : 2019.04.25
  • Published : 2019.05.30
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Abstract

In this paper we construct orthogonal two-direction scaling function of order 3 and corresponding wavelet function. In this paper we propose a different approach using orthogonal symmetric/antisymmetric multiwavelets of order 3. An example for constructing orthogonal two-direction scaling function of order 3 and corresponding wavelet function is given.

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E1MCA9_2019_v37n3_4_307_f0001.png 이미지

FIGURE 3.1. Orthogonal two-direction scaling functions of order 3 and wavelet functions from CL3: (a) φ(x). (b) φ(3 - x).(c) ψ(x). (d) ψ(-3- x).

References

  1. C.K. Chui and J.A. Lian, A study of orthonormal multi-wavelets, Appl. Numer. Math. 20 (1996), 273-298. https://doi.org/10.1016/0168-9274(95)00111-5
  2. S.G. Kwon, Approximation order of two-direction multiscaling functions, Submitted.
  3. S.G. Kwon, Two-direction multiwavelet moments, Appl. Math. Comput. 219 (2012), 3530-3540. https://doi.org/10.1016/j.amc.2012.09.034
  4. S.G. Kwon, Orthogonal two-direction wavelets of order 2 from orthogonal symmetric/antisymmetric multiwavelets, J. Appl. Math. Inform. 35 (2017), 181-189. https://doi.org/10.14317/jami.2017.181
  5. S. Yang, Biorthogonal two-direction refinable function and two-direction wavelet, Appl. Math. Comput. 182 (2006), 1717-1724. https://doi.org/10.1016/j.amc.2006.06.003
  6. S. Yang and Y. Li, Two-direction refinable functions and two-direction wavelets with high approximation order and regularity, Sci. China Ser. A 50 (2007), 1687-1704. https://doi.org/10.1007/s11425-007-0091-7
  7. S. Yang and C. Xie, A class of orthogonal two-direction refinable functions and two-direction wavelets, Int. J. Wavelets Multiresolut. Inf. Process. 6 (2008), 883-894. https://doi.org/10.1142/S0219691308002653