Discrete finite-difference time domain impulse response filters for transparent field source implementations

Closed form discrete transfer functions are derived for finite-difference time domain (FDTD) grids in two- and three-dimensional (3D) space. The transfer functions can be used directly to synthesise the grid impulse response as part of modelling accurate and transparent embedded field sources in FDTD simulations. This approach eliminates the need for measuring grid impulse responses by end users from large and time consuming homogeneous unbounded simulations. The transfer functions were determined through designing fifth order infinite impulse response (IIR) digital filters using a combination of the Prony method and non-linear regression. It was found that the impulse response of equally spaced FDTD grids is independent of absolute values of temporal and spatial steps and rather depends only on the relative ratio of the used time step to the maximum allowed by the stability criterion. Sets of IIR filters are presented and validated for two-dimensional and 3D FDTD grids employing the standard as well as high-order FDTD update equations.