Minimum and maximum time-localized complex-valued wavelets for scattering problems

The authors explore the importance of symmetric or antisymmetric wavelets with compact supports and orthogonal behavior for solving electromagnetic problems. Since there are many wavelets genus can be obtained, either real-valued or complex-valued, we need a reasonable criterion to choose the most suitable basis for the application at hand. A new selection criterion based on the time-localization measure of scaling functions and wavelets is proposed to investigate the relationship between the localization of wavelets and the sparsity of the resultant moment method (MoM) matrix equation.