|
Figure 6
An explanation of the necessity of distribution centring for the approximation with the moments of the second order to be correct. The Fourier transform (black curve in the right-hand figure) of both Gauss distributions (red and blue lines from the left-hand figure) is approximated by the series expansion of the distribution characteristic function. In both cases σ = 3. The approximation for the blue distribution (centred at μ = 0) works better than that for the red distribution (μ = 5). The quicker divergence is observed because the distribution is displaced from the origin of the coordination system, which results in a larger value of the second moment (〈x2〉 = 34). The inverted convexity of the red approximation is caused by the nonzero value of the first moment. |