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The hybrid stripmap/spotlight mode for a synthetic aperture radar (SAR) system is able to generate microwave images with an azimuth resolution better than the one achieved in the stripmap mode and a ground coverage better than the one of the spotlight mode. In this paper, time- and frequency-domain-based procedures to simulate the raw signal in the hybrid stripmap/spotlight mode are presented and compared. We show that a two-dimensional Fourier domain approach, although highly desirable for its efficiency, is not viable. Accordingly, we propose a one-dimensional (1-D) range Fourier domain approach, followed by 1-D azimuth time-domain integration. This method is much more efficient than the time-domain one, so that extended scenes can be considered. In addition, it involves approximations usually acceptable in actual cases. Effectiveness of the simulation scheme is assessed by using numerical examples.