In this paper, we propose to perform a novel discrete implementation of the filtered back projection algorithm. For this, we use a version of the discrete exact Radon transform called the Mojette transform that has been developed in our team for few years. The initial questioning was centered about the angular distribution needed for the continuous Radon reconstruction. Because of the discrete set of angles used in the FBP algorithm, discrete angles issued from Farey's series were used. Our version of the FBP algorithm is compared with the classical FBP algorithm. The choice of the set of projection angles is discussed in order to produce a good and efficient angular sampling. Finally, the very different behaviors between the classical FBP and our algorithm justify our study.