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A new approach for processing stepped chirps in spotlight SAR is presented in this manuscript, which is based on exploiting the principle of chirp scaling (PCS). In particular the PCS is integrated in a polar format algorithm (PFA), obtaining a more efficient solution compared with the existing interpolation based technique. The main contribution is the implementation of the azimuth scaling with the bandwidth synthesis embedded in, and it is developed dedicatedly for dealing with stepped chirps. The signal processing flow is investigated in detail, with no interpolations but only FFT's and complex multiplications involved, and point target simulation has validated the new approach based on PCS is feasible and more efficient than the existing interpolation based approach.