Dealing with the useful window related with the far field pattern

With a convenient representation, the radiation pattern of a spatial distribution of radiating sources is always related with that distribution by a window in the inverse spatial Fourier transform of the distribution. This fact is used to change the distribution of sources without disturbing the radiation pattern. On the other hand, the error, in the mean square sense, made by source elimination is also related with the Fourier transform of the distribution. So it spreads all over the domain and not only inside the useful window. This must be taken in account and, with some signal processing, it is possible to find the error only in the far field pattern using the spatial distributions of sources.