  We present an approximation scheme for functions in three dimensions, that
requires only their samples on the Cartesian grid, under the assumption that
the functions are sufficiently concentrated in both space and frequency. The
scheme is based on expanding the given function in the basis of generalized
prolate spheroidal wavefunctions, with the expansion coefficients given by
weighted dot products between the samples of the function and the samples of
the basis functions. As numerical implementations require all expansions to be
finite, we present a truncation rule for the expansions. Finally, we derive a
bound on the overall approximation error in terms of the assumed
space/frequency concentration.
