A sampling theorem on shift-invariant spaces associated with the fractional Fourier transform domain

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. Keyword: the fractional Fourier transform, shift-invariant space, uniform sampling, reproducing kernel Hilbert space Mathematics Subject Classification (2010) Primary 94A20 · Secondary 42C15