On Nonuniform Sampling of Bandlimited Signals Associated with the Fractional Fourier Transform

The uniform sampling theorem and the reconstruction formulae associated with the fractional Fourier transform (FrFT) have been deduced in the literature, but the nonuniform sampling is yet to receive attention in the fractional Fourier domain. This paper focus on a special kind of non-uniform sampling process associated with the fractional Fourier transform. A nonuniform sampling model is first introduced and then, based on a useful lemma, the reconstruction formula for the nonuniform sampled signal points associated with the fractional Fourier transform is deduced. In addition, the classical results in the Fourier domain can be seen as a special case of our work.