A multiplexing theorem and generalisation of R-transform

Abstract

Analytical properties of Rapid transform are investigated. Transforms of multiplexed patterns are resolved into the transforms of constituent patterns. It is shown that periodicity in pattern domain corresponds to a null subspace in transform domain and a null subspace in pattern domain gives a periodic transform. Further, the nontrivial portion of the transform is related to the transform of the nontrivial portion of the pattern. Based on these properties of R-transform, a generalised R-transformation for rectangular patterns is defined. It displays the translation invariant property of R-transform and reduces to R-transform in case of square and column patterns.