Discrete-time electromagnetic theory

A new theory for solving time-domain electromagnetic field problems is proposed. By this new theory the field is first expanded by bases in time, and the inner product of the equation residue is taken with respect to a set of testing functions to achieve a system of differential equations in space coordinates. The obtained matrix equations can then be either solved analytically, if possible, or numerically. This provides more flexibility in solution. In the special case that all matrices are Toeplitz, which is common if translation-invariant bases are adopted, the z transform is applicable. With the help of z transform theory in digital signal processing, concepts of discrete-time frequency and discrete-time traveling wave are introduced. Dispersion analysis of the central difference approximation as well as the FDTD equation for one-dimensional wave is found easy with this theory.