Simulation of 3-D random rough surface by 2-D digital filter and fourier analysis

2-D FIR filters are applied to the generation of 3-D random surfaces in this paper. The circularly symmetric low-pass filters are firstly employed to generate the isotropic random surfaces with no restrictions on the shape of ACF. To simulate real rough surfaces, however, one has to generate the surfaces having an expected autocorrelation function and height distribution, which requires determining the filter coefficients corresponding to the specified ACF. A spectrum analysis approach is developed in this paper to compute the filter coefficients and the FFT procedure provides an efficient way to implement the filter. The Johnson translator system of distribution is introduced into the generation procedure of non-Gaussian surface with a required ACF. The analysis indicates that the 2-D FIR filters used in this paper are mathematically identical with the 2-D MA time series model which simulates the ACF within whole correlation regions.