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In this paper, the frequency scaling algorithm (FSA) has been introduced for the first time to spaceborne spotlight SAR. According to the characteristics that the range time extension of the observed scene is smaller than the width of the transmitted pulse, FSA applied in airborne spotlight SAR dechirps on received echoes and reduces the sampling rate to release the computational burden. However, in spaceborne SAR, the range extension is much larger and the bandwidth after dechirping increases instead so that the existing FSA cannot be adopted. To solve this problem, a method to perform directly frequency scaling on chirps in the range direction has been proposed. And azimuth compression has also been applied to reduce the pulse repetition frequency in the azimuth direction. Finally, simulation results of point targets are given to demonstrate the validity and efficiency of the proposed algorithm.