1) The document proposes a method using the discrete fractional Fourier transform (DFRFT) to estimate target vibrations from synthetic aperture radar (SAR) imagery. 2) The method was tested on SAR data collected by the Lynx system of a stationary target vibrating at 5 Hz with an amplitude of 1.5 mm. 3) The DFRFT method successfully estimated the target's vibration frequency and reconstructed the time-varying vibration acceleration signal from the SAR data.