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Improving impedance matrix localization by a digital filtering approach

Wavelet bases have been employed recently in numerical solutions of integral equations encountered in electromagnetic scattering problems. The advantage of these bases lies in their ability to render the problem impedance matrix more localized. In this paper, we propose a digital filtering approach for integrating wavelet transforms into existing electromagnetic-scattering numerical-solvers. The suggested approach facilitates a much faster implementation of the transform. It also allows the incorporation of other ideas such as wave-packets and best-basis from the discipline of digital signal processing. A physical interpretation of the basis functions obtained by a few selected structures of digital filters is given, and their usefulness is explained. A numerical example is given for the case of TM scattering by a square cylinder.