Wavelet electromagnetic field processing: Multidimensional fast wavelet transform decomposition of time and frequency domain electromagnetic fields

This paper presents a wavelet processing method for time and frequency domain electromagnetic fields for the rigorous and efficient inspection of the wave physics properties of transient and time-harmonic electromagnetic field solutions. More specifically, this research expounds upon the construction of (discrete) isotropic Fast Wavelet Transform (FWT) decompositions for multidimensional time and frequency domain electromagnetic fields with applications to electromagnetic radiation and scattering. In this work, discretely sampled space-time and space-frequency electromagnetic fields are processed using the (isotropic) Fast Wavelet Transform (FWT) algorithm [5], customized here to address real (IR) and complex (C) valued electromagnetic vector fields. Moreover, the structure and physical interpretation of the wavelet coefficients are described in detail.