Basic concepts of multidimensional space filters

Abstract

The conventional electric network, consisting of linear or one-dimensional RLC (resistance-inductance-capacitance) elements, may be generalized by adding to it planar-, cubic-, etc., up to k-dimensional RLC elements. The resultant geometrical configuration of 0-, 1-, 2-... to k-dimensional spatial networks interconnected into one structure is called, in combinatorial topology, a “polyhedron.” Its electric-network realization may be called a “wave model.” The electromagnetic structure formed by interconnecting two or more wave models into one network, will be called a “multidimensional space filter.” The latter is expected to be employed eventually for the theoretical and perhaps practical solution of such physical problems for which the conventional linear (one-dimensional) electric filter is used today, on a much more elaborate multidimensional scale, of course. A single polyhedron is expected to be used in the numerical solution of simpler multidimensional problems of the calculus of finite differences, having nonuniform space intervals.