A sampling theorem of chirp periodic and non-bandlimited signals from finite set of samples associated with the fractional Fourier transform

Abstract

Recently, Shi et al. constructed a class of function spaces and proposed a sampling theorem without band-limiting constraint for the fractional Fourier transform (FRFT) in this kind of function spaces. The authors also investigated the truncation error of the sampling theorem. In this paper we consider a small class of signals in the function spaces, that is, the chirp periodic signals associated with the FRFT. Then, we deduce a perfect interpolation formula for this type of signals by making use of the Zak transform (ZT), which interpolates the finite set of spaced samples. We also show that the interpolation formula for chirp periodic and bandlimited signals in the FRFT domain from finite number of uniformly spaced samples is a special case of the derived result. Moreover, we present some applications to demonstrate that the proposed reconstruction method achieves better performance than the previous.