A generalized sampling model in shift-invariant spaces associated with fractional Fourier transform

Sampling theories associated with the fractional Fourier transform (FrFT) have blossomed in recent years. However, the majority of the existing sampling models in shift-invariant spaces are constructed using a single generator, which may be inefficient for some mixed signals. In this paper, we first develop a theory for generalized shift-invariant and sampling spaces associated with the FrFT. The conditions and related proof for forming a Riesz basis using the proposed theory are provided. Based on the proposed theory, non-ideal sampling frameworks are constructed using a single generator and multi generators. Furthermore, considering that the non-ideal sampling schemes contain many chirp signal modulators that would increase the hardware complexity and energy consumption, the simplified non-ideal sampling models are also shown in this paper. Finally, the numerical results validate the theoretical derivations.