Multiresolution Time-Domain Using CDF Biorthogonal Wavelets
نویسنده
چکیده
A new approach to the multiresolution time-domain (MRTD) algorithm is presented in this paper by introducing a field expansion in terms of biorthogonal scaling and wavelet functions. Particular focus is placed on the Cohen–Daubechies–Feauveau (CDF) biorthogonal-wavelet class, although the methodology is appropriate for general biorthogonal wavelets. The computational efficiency and numerical dispersion of the MRTD algorithm are addressed, considering several CDF biothogonal wavelets, as well as other wavelet families. The advantages of the biorthogonal MRTD method are presented, with emphasis on numerical issues.
منابع مشابه
Generalized biorthogonal Daubechies wavelets
We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9/7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. We consider a dual pair of such multiresolutions, where the scaling functi...
متن کاملCharacterizations of biorthogonal wavelets which are associated with biorthogonal multiresolution analyses
We improve Wang's characterization for a pair of biorthogonal wavelets to be associated with biorthogonal multiresolution analyses (MRA's). We show that one of the two conditions in his characterization is redundant, and, along the way, show that for a pair of biorthogonal wavelets to be associated with biorthogonal MRA's it is necessary and suÆcient that one of the wavelets is associated with ...
متن کاملScattering Analysis by the Multiresolution Time-Domain Method Using Compactly Supported Wavelet Systems
We present a formulation of the multiresolution time-domain (MRTD) algorithm using scaling and one-level wavelet basis functions, for orthonormal Daubechies and biorthogonal Cohen-Daubechies-Feauveau (CDF) wavelet families. We address the issue of the analytic calculation of the MRTD coefficients. This allows us to point out the similarities and the differences between the MRTD schemes based on...
متن کاملConstruction of biorthogonal wavelets starting from any two multiresolutions
Starting from any two given multiresolution analyses of L2, fV 1 j gj 2Z, and fV 2 j gj 2Z, we construct biorthogonal wavelet bases that are associated with this chosen pair of multiresolutions. Thus, our construction method takes a point of view opposite to the one of Cohen–Daubechies–Feauveau (CDF), which starts from a well-chosen pair of biorthogonal discrete filters. In our construction, th...
متن کاملThree-Dimensional Biorthogonal Multi-Resolution Time-Domain Method and its Application to Electromagnetic Scattering Problems
A three-dimensional multi-resolution time-domain (MRTD) analysis is presented based on a biorthogonal-wavelet expansion, with application to electromagnetic-scattering problems. We employ the Cohen-Daubechies-Feauveau (CDF) biorthogonal wavelet basis, characterized by the maximum number of vanishing moments for a given support. We utilize wavelets and scaling functions of compact support, yield...
متن کامل