In this paper we consider specific features of the fractional Fourier transform (FT) for periodic signals. It is shown that the fractional FT of a periodic signal at some angles is the superposition of its scaled weighted and shifted replicas with additional quadratic phase factor. The modulus of the fractional FT (Radon-Wigner transform) at an angle alpha not equal pi/2 + pi n of a periodic signal is also periodic. For a certain sequence of angles, the Radon-Wigner transforms are affine to each other. This feature simplifies the tomographic reconstruction procedure of periodic signals. (C) 1998 Elsevier Science B.V. All rights reserved.