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In this letter, a novel algorithm based on homomorphic deconvolution is proposed to give a theoretically unbiased estimation of transmitted nonlinearity in the beat signal in frequency-modulated continuous-wave synthetic aperture radar. Transmitted and received nonlinearities in the beat signal are separated in the Cepstrum domain by using a controllable delay line, and the transmitted nonlinearity can be extracted by comb notch filter. Moreover, an integrated nonlinearity correction strategy with residual-video-phase removal is presented by combining with the proposed estimation algorithm. Extensive simulations are performed to validate the generality and the robustness of the proposed algorithm.