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Synthetic aperture radar (SAR) raw signal simulation is a powerful tool for designing new sensors, testing processing algorithms, planning missions, and devising inversion algorithms. In this paper, a spotlight SAR raw signal simulator for distributed targets is presented. The proposed procedure is based on a Fourier domain analysis: a proper analytical reformulation of the spotlight SAR raw signal expression is presented. It is shown that this reformulation allows us to design a very efficient simulation scheme that employs fast Fourier transform codes. Accordingly, the computational load is dramatically reduced with respect to a time-domain simulation and this, for the first time, makes spotlight simulation of extended scenes feasible.