Construction of Complex-Valued Wavelets and Its Applications to Scattering Problems

Jeng-Long LEOU; Jiunn-Ming HUANG; Shyh-Kang JENG; Hsueh-Jyh LI

Construction of Complex-Valued Wavelets and Its Applications to Scattering Problems

Jeng-Long LEOU, Jiunn-Ming HUANG, Shyh-Kang JENG, Hsueh-Jyh LI

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This paper introduces the construction of a family of complex-valued 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, maximum-localized complex-valued wavelets and minimum-localized complex-valued wavelets are investigated. Regularity of root location of the Daubechies polynomial in spectral factorization are also presented to construct these two extreme genus of complex-valued 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 real-valued Daubechies wavelets, minimum-localized complex-valued Daubechies and maximum-localized complex-valued 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.

Publication: IEICE TRANSACTIONS on Communications Vol.E83-B No.6 pp.1298-1307

Publication Date: 2000/06/25

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Jeng-Long LEOU, Jiunn-Ming HUANG, Shyh-Kang JENG, Hsueh-Jyh LI, "Construction of Complex-Valued Wavelets and Its Applications to Scattering Problems" in IEICE TRANSACTIONS on Communications, vol. E83-B, no. 6, pp. 1298-1307, June 2000, doi: .
Abstract: This paper introduces the construction of a family of complex-valued 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, maximum-localized complex-valued wavelets and minimum-localized complex-valued wavelets are investigated. Regularity of root location of the Daubechies polynomial in spectral factorization are also presented to construct these two extreme genus of complex-valued 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 real-valued Daubechies wavelets, minimum-localized complex-valued Daubechies and maximum-localized complex-valued 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.
URL: https://global.ieice.org/en_transactions/communications/10.1587/e83-b_6_1298/_p

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@ARTICLE{e83-b_6_1298,
author={Jeng-Long LEOU, Jiunn-Ming HUANG, Shyh-Kang JENG, Hsueh-Jyh LI, },
journal={IEICE TRANSACTIONS on Communications},
title={Construction of Complex-Valued Wavelets and Its Applications to Scattering Problems},
year={2000},
volume={E83-B},
number={6},
pages={1298-1307},
abstract={This paper introduces the construction of a family of complex-valued 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, maximum-localized complex-valued wavelets and minimum-localized complex-valued wavelets are investigated. Regularity of root location of the Daubechies polynomial in spectral factorization are also presented to construct these two extreme genus of complex-valued 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 real-valued Daubechies wavelets, minimum-localized complex-valued Daubechies and maximum-localized complex-valued 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.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - Construction of Complex-Valued Wavelets and Its Applications to Scattering Problems
T2 - IEICE TRANSACTIONS on Communications
SP - 1298
EP - 1307
AU - Jeng-Long LEOU
AU - Jiunn-Ming HUANG
AU - Shyh-Kang JENG
AU - Hsueh-Jyh LI
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Communications
SN -
VL - E83-B
IS - 6
JA - IEICE TRANSACTIONS on Communications
Y1 - June 2000
AB - This paper introduces the construction of a family of complex-valued 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, maximum-localized complex-valued wavelets and minimum-localized complex-valued wavelets are investigated. Regularity of root location of the Daubechies polynomial in spectral factorization are also presented to construct these two extreme genus of complex-valued 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 real-valued Daubechies wavelets, minimum-localized complex-valued Daubechies and maximum-localized complex-valued 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.
ER -