Basic concepts of multidimensional space filters

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics

Vol. 78 (5) , 554-561
https://doi.org/10.1109/tce.1959.6372861

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.

Keywords

This publication has 0 references indexed in Scilit: