Approximations in Fourier Transforms

The Fourier transform is a necessary tool for translation between the time-function and frequency-function description of a waveform, or between linear distribution of intensity across an aperture and angular distribution of radiation from the aperture. If the function to be transformed is of reasonably simple analytical form, there is no difficulty: one has merely to consult a table of Fourier transforms such as was produced by Campbell and Foster (1948). But if the subject to be transformed is a set of experimental data, not conforming precisely to any analytical law, the problem is less easy. The direct approach is to perform numerically "the integration