Methods and Algorithms for Horizontal Sliding Spatial-Frequency Fourier Processing of Two-Dimensional Discrete Finite Signals

Abstract

The method of horizontal sliding two-dimensional discrete Fourier transform, is proposed. The mathematical apparatus of direct two-dimensional discrete Fourier transform in algebraic and matrix form is considered. The stages of performing two-dimensional discrete Fourier transform using one-dimensional fast Fourier transform are considered. An efficient method and algorithm for the horizontally sliding transform are developed. The method allows the calculation of the coefficients of this transform in real time. The effectiveness of horizontal sliding two-dimensional discrete Fourier transform algorithm was evaluated in terms of computational cost in comparison with known algorithms. As a result of experimental investigations on model two-dimensional discrete signals, the validity, efficiency and reliability of the proposed method and algorithm of horizontally sliding two-dimensional discrete Fourier transform have been proved. The developed method of horizontally sliding two-dimensional discrete Fourier transform has been compared to the standard method of obtaining coefficients of two-dimensional discrete transform in terms of computational costs. The surfaces of relative economy of computations in the developed algorithm in comparison with the standard algorithm of horizontal sliding processing of two-dimensional discrete signals are plotted.