On bandlimited signals with fractional Fourier transform

In this letter, we study bandlimited signals with fractional Fourier transform (FRFT), We show that if a nonzero signal f is bandlimited with FRFT F-alpha for a certain real alpha, then it is not bandlimited with FRFT F-beta for any beta with beta not equal +/-alpha + n pi for any integer n. This is a generalization of the fact that a nonzero signal can not be both timelimited and bandlimited, We also provide sampling theorems for bandlimited signals with FRFT that are similar to the Shannon sampling theorem.