Analysis of Multiplex Systems Based on Orthonormal Function Groups

Abstract

Linear multiplex systems may be represented as sequential, invertible transformations on a message set. Such transformations are based on orthonormal functions in the Hilbert space of square-integrable functions. Demultiplexing is accomplished with the inner product which results in high immunity to noise and bandlimiting. When the orthonormal functions form a multiplicative group, easily generated pulse functions arise. Methods are presented for determining these function groups and their corresponding algebras which yield simple and useful multiplex systems.