A new method for processing multidimensional signals using \(R\)-functions and atomic functions (Q1420643)

Application of atomic functions for digital processing of one-dimensional signals was described in the previous papers of the first author. But many operations of the one-dimensional processing can be transposed to the multidimensional case. It turns out that using an operation of a direct product or rotation of one-dimensional windows it is possible to synthesize multidimensional atomic windows with a rectangular hexagonal or circular aperture. There are some difficulties both of qualitative and quantitative kind when the windows of an arbitrary reference domain are used. The difficulties are caused by the necessity of an analytic description of the windows geometry. In the article it is shown that a solution of the problem can be found by using R- and atomic functions.