ORTHOGONAL WAVELETS WITH APPLICATIONS IN ELECTROMAGNETICS

A topic of considerable current interest in applied mathematics is wav elets. The promises of wavelets are based upon their localization in b oth spatial and spectral domains, better convergence properties, their computational speed, and the two parameter invariance under analytic representations. Recently Wavelets have been used in signal processing slid computer vision with great success. In electromagnetics (EM), or thonormal wavelets have been applied to the method of moments as basis and testing functions in the integral equations to replace the pulse, triangle, and PWS (piecewise sinusoidal) functions. Very sparse coeff icient matrices have been obtained due to the vanishing moments, local ization, and MRA (multiresolution analysis) of the wavelets. In this p aper we introduce the basic wavelet theory, summarize the wavelet prop erties and present the applications of orthogonal wavelets to the eddy current and EM wave scattering problems.