We implement numerically formulas of [Isaev, Novikov, arXiv:2107.07882, hal-03289374] for finding a compactly supported function v on R^d , d ≥ 1, from its Fourier transform F[v] given within the ball B_r. For the one-dimensional case, these formulas are based on the theory of prolate spheroidal wave functions, which arise, in particular, in the singular value decomposition of the aforementioned band-limited Fourier transform for d = 1. In multidimensions, these formulas also include inversion of the Radon transform. In particular, we give numerical examples of super-resolution, that is, recovering details beyond the diffraction limit.