Browsing by Author "Jeng, SK"

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Application of mix-phase wavelets to sparsify impedance matrices
(1999-10-01)
Huang, JM
;
Leou, JL
;
Jeng, SK
;
Tarng, JH
;
電信工程研究所
Effective wavelets to solve electromagnetic integral equations are proposed. It is based on the same construction procedure as Daubechies wavelets but with mix-phase to obtain maximum sparsity of moment matrix. These new wavelets are proved to have excellent performance in non-zero elements reduction in comparison with minimum-phase wavelet transform (WT). If further sparsity is concerned, wavelet packet (WP) transform can be applied but increases the computational complexity. In some eases, the capability of non-zero elements reduction by this nsw wavelets even better than WP with minimum-phase wavelets and with less computational efforts. Numerical experiments demonstrate the validity and effectiveness of the neu; wavelets.
Application of wavelets to scattering problems of inhomogeneous dielectric slabs
(1999-10-01)
Leou, JL
;
Huang, JM
;
Jeng, SK
;
Li, HJ
;
電信工程研究所
In this paper, we apply the discrete wavelet transform (DWT) and the discrete wavelet packet transform (DWPT) with the Daubechies wavelet of order 16 to effectively solve for the electromagnetic scattering from a one-dimensional inhomogeneous slab. Methods based on the excitation vector and the [Z] matrix are utilized to sparsify an MoM matrix. As we observed, there are no much high frequency components of the field in the dielectric region, hence the wavelet coefficients of the small scales components (high frequency components) are very small and negligible. This is different from the case of two-dimensional scattering from perfect conducting objects. In the excitation-vector-based method, a modified excitation vector is introduced to extract dominant terms and achieve a better compression ratio of the matrix. However, a smaller compression ratio and a tiny relative error are not obtained simultaneously owing to their deletion of interaction between different scales. Hence, it is inferior to the [Z]-matrix-based methods. For the [Z]-marix-based methods, our numerical results show the column-tree-based DWPT method is a better choice to sparsify the MoM matrix than DWT-based and other DWPT-based methods. The cost of a matrix-vector multiplication for the wavelet-domain sparse matrix is reduced by a factor of 10, compared with that of the original dense matrix.
Construction of complex-valued wavelets and its applications to scattering problems
(2000-06-01)
Leou, JL
;
Huang, JM
;
Jeng, SK
;
Li, HJ
;
電信工程研究所
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.
Impedance matrix compression using an effective quadrature filter
(2000-08-01)
Huang, JM
;
Leou, JL
;
Jeng, SK
;
Tarng, JH
;
電信工程研究所
An effective quadrature mirror filter (QMF) proposed by Vaidyanathan has been used to solve 2D scattering problems. QMF has been popular for some time in digital signal processing, under the names of multirate sampling, wavelets, etc. In this work, the impulse response coefficients of QMF were used to construct the wavelet transform matrix. Using the matrix to transform the impedance matrices of 2D scatterers produces highly sparse moment matrices that can be solved efficiently. Such a presentation provides better sparsity than the celebrated and widely used Daubechies wavelets. These QMF coefficients are dependent on the filter parameters such as transition bandwidth and filter length. It was found that the sharper the transition bandwidth, the greater the reduction in nonzero elements of the impedance matrix. It also can be applied in the wavelet packet algorithm to further sparsify the impedance matrix. Numerical examples are given to demonstrate the effectiveness and validity of our finding.