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Construction of ComplexValued Wavelets and Its Applications to Scattering Problems
JengLong LEOU JiunnMing HUANG ShyhKang JENG HsuehJyh LI
Publication
IEICE TRANSACTIONS on Communications
Vol.E83B
No.6
pp.12981307 Publication Date: 2000/06/25 Online ISSN:
DOI: Print ISSN: 09168516 Type of Manuscript: PAPER Category: FiberOptic Transmission Keyword: complexvalued wavelets, Daubechies polynomial, maximumlocalized, minimumlocalized, scattering,
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Summary:
This paper introduces the construction of a family of complexvalued scaling functions and wavelets with symmetry/antisymmetry, compact support and orthogonality from the Daubechies polynomial, and applies them to solve electromagnetic scattering problems. For simplicity, only two extreme cases in the family, maximumlocalized complexvalued wavelets and minimumlocalized complexvalued wavelets are investigated. Regularity of root location of the Daubechies polynomial in spectral factorization are also presented to construct these two extreme genus of complexvalued wavelets. When wavelets are used as basis functions to solve electromagnetic scattering problems by the method of moment (MoM), they often lead to sparse matrix equations. We will compare the sparsity of MoM matrices by the realvalued Daubechies wavelets, minimumlocalized complexvalued Daubechies and maximumlocalized complexvalued Daubechies wavelets. Our research summarized in this paper shows that the wavelets with smaller signal width will result in a more sparse MoM matrix, especially when the scatterer is with many corners.

