Dipole Field Representation in Discrete Basis

The dipole electromagnetic field with any temporal and spatial dependence is represented by a couple of two specific time and space-limited functions. The functions are expanded in terms of discrete basis of Hermite-Gaussian functions. The dipole electromagnetic field is calculated applying electric and magnetic Hertzian vectors which temporal dependencies are expressed in finite or infinite summation of Hermite-Gaussian functions. The calculation of radiated time and space-limited dipole fields produced by a given Hertzian vector expressed in terms of the couple introduced function are presented and their properties are discussed.