Sliding Spatial Frequency Processing of Discrete Signals

Abstract

The definition of sliding spatial-frequency processing of discrete signal is given. Fast methods for analyzing two-dimensional discrete signals in the spatial-frequency domain are proposed. The mathematical apparatus of direct two-dimensional discrete Fourier transform in the algebraic and matrix forms is considered. A step by step implementation of two-dimensional discrete Fourier transform based on one-dimensional fast Fourier transform is considered. Effective methods and algorithms for horizontally sliding two-dimensional discrete Fourier transform have been developed that allow us to calculate the coefficients of this transform in time. The developed algorithms efficiency (in terms of computational costs) of real horizontally sliding two-dimensional discrete Fourier transform is evaluated in comparison with the known algorithms. As a result of experimental studies on model two-dimensional discrete signals, the validity, efficiency, and reliability of the proposed methods and algorithms for horizontally sliding two-dimensional discrete Fourier transform have been proved. The relative saving of computations in the developed fast algorithms of horizontal sliding two-dimensional discrete Fourier transform was compared with the standard algorithm.