Ways to improve the accuracy of the harmonic method for simulating two-dimensional signals

The article studies properties of the harmonic simulation method within the framework of the spectral theory and evaluates the quality of this method. A review of the literature on the existing methods for modeling multidimensional random fields is carried out, making it possible to compare these methods using criteria such as the complexity of the algorithm, computational costs and memory requirements, requirements for the covariance function and the grid. Weaknesses are revealed, such as insufficient accuracy and high computational complexity, which are characteristic of spectral simulation methods in general, including the harmonic method. An analysis of forms of the signal simulated by the harmonic method for different bases reveals a property of centrosymmetry for square signals in the Fourier basis, a similar property for rectangular signals in the Fourier basis, the symmetry property of a square signal in the Hartley basis and the absence of such properties for a rectangular signal simulated in the Hartley basis. A comparative analysis of the accuracy of simulating two-dimensional signals, as a special case of multidimensional ones, is carried out by the harmonic method in the Fourier and Hartley bases. It is shown that, depending on the sampling characteristics, the simulated signal in the Fourier basis differs from the same signal simulated in the Hartley basis in terms of accuracy. As a result of the study, recommendations are worked out for choosing the basis in a specific problem of simulating two-dimensional signals. The effect of the discovered properties on the computational complexity of the method is described. Methods for applying these properties to simulate arbitrary two-dimensional signals are proposed.