Niobium surfaces are commonly electropolished in an effort to obtain optimal smoothness for high-field superconducting radio-frequency cavity applications. We report the use of controlled electrochemical analysis techniques to characterize electropolishing of Nb in a sulfuric and hydrofluoric acid electrolyte. Through the use of a reference electrode, we are able to clearly distinguish the anode and cathode polarization potentials as well as the electrolyte voltage drop, which together sum to the applied power supply voltage. We then identify the temperature and HF concentration dependence of each potential. We also report the use of electrochemical impedance spectroscopy (EIS) on this system. EIS results are consistent with the compact salt film mechanism for niobium electropolishing (EP) in this electrolyte and are not consistent with either the porous salt film or the absorbate-acceptor mechanism. Microscopic understanding of the basic Nb EP mechanism is expected to provide an appropriate foundation with which to optimize the preparation of high-field niobium cavity surfaces. (C) 2008 The Electrochemical Society.