  As a generalization of the Fourier transform, the fractional Fourier
transform was introduced and has been further investigated both in theory and
in applications of signal processing. We obtain a sampling theorem on
shift-invariant spaces associated with the fractional Fourier transform domain.
The resulting sampling theorem extends not only the classical
Whittaker-Shannon-Kotelnikov sampling theorem associated with the fractional
Fourier transform domain, but also extends the prior sampling theorems on
shift-invariant spaces.
