Calculation of Fourier Integrals (D1).

The article presents information about a method for computing Fourier integrals by using algorithm 418. The most commonly used formula for calculating Fourier integrals is Filon's formula. The formula is based on the approximation of the function by a quadratic equation in each double interval. In order to obtain a better approximation, the cube spline fit is used. The obtained formulas do not need the explicit calculation of the spline fit. However, in addition to the function values, at all intermediate points, the values of the first and second derivatives at the boundary points are required. However, these values are often obtained from symmetry conditions. If the derivatives at the end points are unknown, they may be calculated from a cubic spline fit, for example by using some exterior points or by using two extra interior conditions for the spline fit. It can also be noted that in certain periodic cases the terms containing the derivatives will cancel and their vales will be superfluous.