This paper describes a novel method based on the back-projection approach to generate SAR images. The back-projection operation has various 'fast' implementations all using multilevel algorithms. In this paper a back-projection algorithm using the Fast Fourier Transform (FFT) is proposed. The basic method does not employ interpolation by using non uniform sampling, and it obtains the same results as the straightforward computation, with O(N2logN) instead of O(N4) complexity. This method is optimal for SPOT mode and for wide-band scenarios, however to expand the algorithm flexibility two additional implementations are presented. As opposed to the basic method which does not use interpolation at all, these implementations require interpolation in the imaging process, but the error introduced is negligible.