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.
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