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

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

Publication
IEICE TRANSACTIONS on Communications   Vol.E83-B   No.6   pp.1298-1307
Publication Date: 2000/06/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Fiber-Optic Transmission
Keyword: 
complex-valued wavelets,  Daubechies polynomial,  maximum-localized,  minimum-localized,  scattering,  

Full Text: PDF>>
Buy this Article




Summary: 
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.