Discrete Simulation of Uniform Transmission Lines by Multidimensional Digital Filters

Abstract

Recently, a new method has been presented for the discrete simulation of multidimensional systems, which are described by linear partial differential equations with constant coefficients. It is based on methods customary in linear systems theory and digital signal processing and uses a frequency‐domain representation of the continuous system to be simulated. A proper choice of functional transformations for each independent variable allows us to treat the influence of initial conditions, boundary conditions and excitation functions separately by suitable transfer functions. From these, corresponding discrete transfer functions and the structure of a discrete system for the simulation of the continuous problem are derived. The application of this method to wave propagation problems on uniform transmission lines is presented here. At first, the continuous problem is characterized by transfer functions; then the derivation of a discrete system is shown, and finally, some simulation results and a comparison with other methods are given.

Transfer Function Models for Multidimensional Systems with Bounded spatial Domains

“…The other direction leads to a discrete-time and discrete-space model suitable for computer simulation and is shortly described here. Details of the transition from continuous to discrete transfer function models have already been reported [12,14,15,16,17,18,19]. Thus a brief account of the main topics is sufficient.…”