  We describe a method for the calculation of photoionization cross-sections
using square-integrable amplitudes obtained from the diagonalization of
finite-basis set representations of the electronic Hamiltonian. Three examples
are considered: a model example in which the final state is a free particle,
the hydrogen atom and neutral atomic sodium. The method exploits the
Whittaker-Shannon-Kotel'nikov sampling theorem, which is widely used in digital
signal sampling and reconstruction. The approach reproduces known data with
very good accuracy and converges to the exact solution with increase of the
basis set size.
