The Doppler frequency shift of HF radio waves vertically reflected from the ionosphere is related to the apparent velocity profile of the reflecting layer through an integral equation. An algorithm is proposed to solve this equation when simultaneous measurements of the Doppler shift at several frequencies are available. This permits one to recover the apparent velocity profile from Doppler data. In order to test the theory, a vertical Doppler sounder has been built which can explore sequentially several preselected probing frequencies in the HF band. This sounder is composed of currently available laboratory equipment controlled by a desk top computer. A comparison has been performed between the Doppler results and the St-Santin incoherent scatter data. Though obtained from a limited amount of data, experimental evidence seems to support the theory. Conditions for the applicability of the method are discussed.