  Let $f$ be a Paley-Wiener function in the space $L_{2}(X)$, where $X$ is a
symmetric space of noncompact type. It is shown that by using the values of $f$
on a sufficiently dense and separated set of points of $X$ one can give an
exact formula for the Helgason-Fourier transform of $f$. In order to find a
discrete approximation to the Helgason-Fourier transform of a function from a
Besov space on $X$ we develop an approximation theory by Paley-Wiener functions
in $L_{2}(X)$.
