Fast Method of Diagonal Sliding Spatial-Frequency Fourier Processing of Discrete Finite Signals

Abstract

The new method of digital Fourier processing of two-dimensional discrete finite signals as fast algorithm of diagonal sliding two-dimensional discrete Fourier transform is offered in the paper. The developed method of digital Fourier processing of two-dimensional finite signals is a generalization of the one-dimensional sliding discrete Fourier transform to the two-dimensional case. The fast algorithm of the diagonal-sliding two-dimensional discrete Fourier transform is developed based on the mathematical apparatus of the direct two-dimensional discrete Fourier transform in matrix and algebraic form. The algorithm of diagonal-sliding two-dimensional discrete Fourier transform, due to the recurrence structure, allows to realize a real time scale processing of two-dimensional signals in the spatial-frequency domain. The paper presents the results of a comparative analysis of the proposed algorithm for the diagonal-sliding two-dimensional discrete Fourier transform of two-dimensional finite signals with the standard algorithms of sliding diagonal digital processing. The comparison, carried out according to the criteria of validity, efficiency and reliability, showed the advantages of the diagonal-sliding two-dimensional discrete Fourier transform algorithm. Based on the results of mathematical modeling, the article graphically presents the relative computational savings provided by the proposed algorithm for diagonal-sliding two-dimensional discrete Fourier transform in comparison with known algorithms.