Transfer function models for continuous and discrete multidimensional systems

Continuous multidimensional systems, which are described by partial differential equations are usually discretized by standard methods from numerical mathematics. Here, a general approach for the transfer function description of multidimensional systems is presented. It allows a correct representation of initial and boundary values also for problems with spatially varying coefficients, general boundary conditions, three spatial dimensions and general differentiation operators. In spite of this generality, the resulting discrete systems can be realized with standard signal processing elements and are free of implicit loops.