Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A NOTE ON THE PARAMETRIZATION OF MULTIWAVELETS OF DGHM TYPE

  • Received : 2010.07.23
  • Accepted : 2010.10.11
  • Published : 2011.05.30
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Abstract

Multiwavelet coefficients can be constructed from the multi-scaling coefficients by using the factorization for paraunitary matrices. In this paper we present a procedure for parametrizing all possible multi-wavelet coefficients corresponding to the multiscaling coefficients of DGHM type.

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References

  1. I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1998), 909-996.
  2. I. Daubechies, Ten lectures on wavelets, SIAM, Philadelphia, 1992.
  3. G.C. Donovan, J.S. Geronimo and D.P. Hardin, Intertwining multiresolution analyses and construction of piecewise polynomial wavelets, SIAM J. Math. Analysis 27 (1996), 1791- 1815. https://doi.org/10.1137/S0036141094276160
  4. G.C. Donovan, J.S. Geronimo and D.P. Hardin, Orthogonal multiwavelet constructions : 101 things to do with a hat function, Advances in wavelets, Springer (1999), 187-197.
  5. G.C. Donovan, J.S. Geronimo and D.P. Hardin, Orthogonal polynomials and the construc- tion of piecewise polynomial smooth wavelets, SIAM J. Math. Analysis 30 (1999), 1029- 1056. https://doi.org/10.1137/S0036141096313112
  6. G.C. Donovan, J.S. Geronimo, D.P. Hardin and P.R. Massopust, Construction of orthogonal wavelets using fractal interpolation functions, SIAM J. Math. Analysis 27 (1996), 1158- 1192. https://doi.org/10.1137/S0036141093256526
  7. J.S. Geronimo, D.P. Hardin and P.R. Massopust, Fractal functions and wavelet expansions based on several scaling functions, J. Approx. Theory 78 (1994), 373-401. https://doi.org/10.1006/jath.1994.1085
  8. T.N.T. Goodman and S.L. Lee, Wavelets of multiplicity r, Trans. Amer. Math. Soc. 342 (1994), 307-324.