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Frequency-modulated continuous wave (FMCW) synthetic aperture radar (SAR) system is widely used for earth observation and space detection, where short revisits time at low cost are desirable, or small size is required. Therefore a FMCW SAR raw signal simulator is required to quantitatively support the design of a SAR mission operating in the FMCW mode, to help mission planning, test processing algorithms and analyse jamming and noises. Time-domain SAR raw signal simulation can be easily conceived, but it is extremely time and memory consuming. In this study, an efficient FMCW SAR raw signal simulation approach for extended scene is proposed based on chirp-Z transform (CZT). This is the first time that a FMCW SAR simulator is proposed in the two-dimensional frequency domain. By taking advantage of fast Fourier transform, the proposed approach highly reduces the computational load with respect to the time domain approach. Furthermore, CZT algorithm can accurately simulate the range-variation of the range cell migration term, which guarantees the precision of the proposed approach. Wavenumber domain algorithm is applied to focus the conceived raw signal. Finally, point targets, the electromagnetic imaging and real FMCW image are used to validate the proposed simulation approach.