For synthetic aperture radar (SAR) imaging with the high-frequency band, such as the terahertz band, the platform vibration influence cannot be neglected. In general, the vibration of the platform can be viewed as a simple harmonic motion, and thus, the received signal in each range bin can be considered as a sinusoid frequency modulation (SFM) signal for the terahertz SAR imaging. This will introduce the images to be defocused in the azimuth processing. In this letter, a novel algorithm for the analysis of the SFM signal based on the adaptive chirplet decomposition is proposed. This algorithm is accurate, efficient, and easy to be implemented. Then, the high-frequency vibration of the platform can be compensated by the corresponding signal decomposition results. The simulated results demonstrate the effectiveness of the novel algorithm proposed in this letter.