The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
본 논문에서는 Daubechies 다항식의 대칭/반대칭, 컴팩트 지원 및 직교성을 갖춘 복소수 스케일링 함수 및 웨이블릿 제품군의 구성을 소개하고 이를 적용하여 전자기 산란 문제를 해결합니다. 단순화를 위해 계열의 두 가지 극단적인 경우인 최대 지역화 복소수 값 웨이블릿과 최소 지역화 복소수 값 웨이블릿만 조사합니다. 스펙트럼 분해에서 Daubechies 다항식의 근 위치 규칙성은 복소수 값 웨이블릿의 두 극단 유형을 구성하기 위해 제시됩니다. MoM(모멘트 방법)으로 전자기 산란 문제를 해결하기 위해 웨이블릿을 기본 함수로 사용하면 종종 희소 행렬 방정식이 생성됩니다. 실수 값 Daubechies 웨이블릿, 최소 지역화 복소수 값 Daubechies 및 최대 지역화 복소수 값 Daubechies 웨이블릿을 통해 MoM 행렬의 희소성을 비교할 것입니다. 이 논문에 요약된 우리의 연구는 신호 폭이 더 작은 웨이블릿이 특히 산란 장치에 모서리가 많은 경우 더 희박한 MoM 행렬을 생성한다는 것을 보여줍니다.
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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},}
부
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 -