Evaluation of Fourier transforms by a Fourier synthesis method

A convenient numerical method is developed for evaluating the Fourier transforms of arbitrary functions by the use of Beevers-Lipson strips. A detailed procedure is worked out for the determination of the radial distribution curve of an amorphous material from the X-ray diffraction intensity curve, but the method is generally applicable provided that the transformed function is continuous and approaches zero sufficiently rapidly. For the purpose considered, strips giving values of A sin 2nx at intervals of in x to two-figure accuracy and extending up to the 45th harmonic are shown to be suitable. The accuracy of the method has been tested by evaluating the transforms of the first three odd Hermite functions with satisfactory results.