Sampling of Sparse Signals in Fractional Fourier Domain

In this paper, we formulate the problem of sampling sparse signals in fractional Fourier domain. The fractional Fourier transform (FrFT) can be seen as a generalization of the classical Fourier transform. Extension of Shannon’s sampling theorem to the class of signals which are fractional bandlimited shows its association to a Nyquist-like bound. Thus proving that signals that have a non-bandlimited representation in FrFT domain cannot be sampled. We prove that under suitable conditions, it is possible to sample sparse (in time) signals by using the Finite Rate of Innovation (FRI) signal model. In particular, we propose a uniform sampling and reconstruction procedure for a periodic stream of Diracs, which have a nonbandlimited representation in FrFT domain. This generalizes the FRI sampling and reconstruction scheme in the Fourier domain to the FrFT domain.