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In inverse synthetic aperture radar (ISAR) imaging of targets with complex motion such as the high maneuvering airplanes and fluctuating ships with oceanic waves, the azimuth echo signals can be modeled with cubic chirps after translational motion compensation, and then, the azimuth focusing quality will be deteriorated by the time-varying chirp rate. In this paper, a parameter estimation method of cubic chirps is proposed based on the discrete chirp Fourier transform (DCFT), which is generated from DCFT for quadratic chirps. Several properties of DCFT for cubic chirps are derived, and we show that the modified DCFT (MDCFT) is more appropriate to deal with the practical applications (e.g., ISAR imaging) than the original DCFT. Therefore, we put forward the imaging algorithm based on MDCFT, and then, simulation results confirm the validity of the proposed algorithm.