Walking tests can provide an indicator of balance and fragility of people. They measure the gait speed and compare it to reference values related to various pathologies. We propose a radar sensor system that allows the evaluation of the gait speed in these tests in an automatic manner. The proposed approach consists of three phases; a first phase where the system automatically distinguishes the three sections of the test, namely walk #1, turn, and walk #2. Then, a second phase where the obtained signal is processed to evaluate the gait speed of the person. This is done through time-frequency analysis of the radar signal. In order to deal with the non-stationary nature of the radar signals, we consider the short-time Fourier transfer in our time-frequency analysis. The third phase consists in segmenting each walk into three segments, namely an acceleration zone, a measured-gait zone, and a deceleration zone. We provide a segmentation of the walking in order to automatically distinguish these zones. The proposed approach is validated using a Vicon motion-capture system, with a mean RMSE equal to 0.076 m/s. As compared to traditional techniques, our proposed system is automatic and does not require acceleration and deceleration zones.