On discretization error of image spectrum restoration

Image processing in discrete systems assumes an application of digital filtration methods and the spectral analysis using discrete (fast) fourier transformation. In many applied problems the error brought by a processing method or a computing system, is comparable with the error of final result getting, the matter of extent of an error of data discretization therefore is topical. The problem of definition of the relative error of discretization of fourier transformation is solved in the offered paper. It is shown that for considered types of real signals the discretization error decreases in inverse proportion to the squared number of discrete points. For some simple types of functions exact expressions for discrete spectrum and the approached expressions of discretization error corresponding to them are received at the big number of points.