Mechanical vibration or rotation of a target or structures on the target may induce additional frequency modulations on the returned radar signal which generate sidebands about the target's Doppler frequency, called the micro-Doppler effect. Micro-Doppler signatures enable some properties of the target to be determined. In the paper, the micro-Doppler effect in radar is introduced and the mathematics of micro-Doppler signatures is developed. Computer simulations are conducted and micro-Doppler features in the joint time -frequency domain are exploited.