Multi-Dimensional Rajan Transform

Abstract

In this paper we describe the formulation of a novel transform called Multi-Dimensional Rajan Transform which is an extension of Rajan Transform Basically Rajan Transform operates on a number sequence whose length is a power of two It transforms any sequence of arbitrary numbers into a sequence of interrelated numbers As regards 2D Rajan Transform there are two methods to implement it i Row- Column method and ii Column-Row method The 2D Rajan Transform obtained using the first method need not be the same as that obtained using second method Similarly one can implement 3-D Rajan Transform using the following approaches i Row-Column-Depth approach ii Row-Depth- Column approach iii Column-Row-Depth approach iv Column-Depth-Row approach v Depth-Row-Column approach and vi Depth- Column-Row approach This paper explains these approaches to implement two and three dimensional Rajan Transforms