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

The method of vertical sliding processing of two-dimensional discrete signals in the spatial-frequency domain is proposed. The method of fast vertical sliding two-dimensional discrete Fourier transform is considered. Based on the analysis of properties of two-dimensional discrete Fourier transform, the method of its two-stage finding based on one-dimensional fast Fourier transform is considered. An effective method for implementing the transform is proposed. The algorithm developed within the proposed method makes it possible to calculate the coefficients (bins) of the transform in real time. The efficiency of the algorithm of the transform under consideration in terms of computational costs in comparison with known algorithms has been evaluated. Experimental studies carried out on model two-dimensional discrete signals showed the validity, efficiency, and reliability of the proposed method and algorithm. The surfaces of relative economy of calculations in the developed algorithm in comparison with the standard algorithm of vertically sliding processing of two-dimensional discrete signals are constructed.