Order evaluation to new elementary operation approach for MIMO multidimensional systems

A new elementary operation approach (NEOA) for Roesser model realisation of multi-input and multi-output (MIMO) multidimensional (n-D) systems has been recently proposed, which can generate a lowest possible realisation but requires trying different processing manners for various possible realisations with different structures and orders. This paper develops two kinds of novel order evaluation methods and the corresponding algorithms for the realisation procedures A and B of the NEOA, respectively, such that the best processing manner for the lowest possible realisation can be determined with much less computational complexity. These new results enable us, for the first time, to know exactly the order of a realisation before actually conducting the realisation, and thus provide us a novel and high-efficiency way to explore the lowest possible realisation problem for MIMO n-D systems. Examples are given throughout this paper to illustrate the main idea as well as effectiveness of the proposed methods.