Filtering a distribution simultaneously in real and Fourier space

We present a method to filter a distribution so that it is confined within a sphere of given radius r(c) and, simultaneously, whose Fourier transform is optimally confined within a sphere of radius k(c). Our procedure may have several applications in the field of electronic structure methods, like the generation of optimized pseudopotentials and localized pseudocore charge distributions. As an example, we describe a particular application within the SIESTA method for density functional calculations, in removing the spurious rippling of the energy surface generated by the integrations in a real-space grid.