Methods of multidimensional signal processing under toroidal coordinate systems

Abstract

Methods of multidimensional signal processing under spatial toroidal coordinate systems configured on a set of combining sums over vector "Glory to Ukraine Star" combinatorial configurations. Base vectors are discussed, and the two theoretically grounded approaches to formation such coordinate systems in order for optimum encoding and conversion of vector signals using its unique properties, both optimum monolithic and group vector codes, and non-redundant codes are proposed. On the particular examples described the benefits of each method of coding of multidimensional signals pointing to corresponding theorems, calculations and illustrative material. Extension of the “star” combinatorial configurations opens new possibilities for the application of methods of optimized coding and processing of multidimensional signals under toroidal coordinate systems for designing modern systems of communication and development of optimized vector information technologies. The remarkable technical merits of the vector configurations, which properties hold for the same set of an optimum encoded design in varieties permutations of its terms is demonstrated, and methods for processing of two- or multidimensional vector signals based on both the optimum binary monolithic and non-redundant codes are presented. Proposed methods of multidimensional signal processing under toroidal coordinate systems provide, essentially, a new approach to generalize them to great class of optimized problems in radio-telecommunications, navigation and information technology. Moreover, the optimization embedded in the underlying combinatorial configurations. The favorable qualities of the "stars" provide breakthrough opportunities to apply them to numerous branches of science and advanced technology, with direct applications to vector data telecommunications, vector encoded design, and optimal vector information technology.