A comparison is carried out between the phase derivative of broadband reflectometry signals, which are cosine signals calculated from a given electron-density profile according to the model that underlies the functioning of broadband reflectometers, and the phase derivative of the corresponding analytic signals. A class of density profiles commonly employed to model high-temperature plasmas is considered, for which it is shown that the two phase derivatives agree well, except for some oscillatory behavior at the beginning and ending of the signals. Gibbs' phenomenon, associated with the practical calculation of the analytic signal is identified as the cause of this effect. The reconstructed density profiles are shown to be practically unaffected by the oscillations, which are averaged out upon integration, leading to good agreement with the original density profiles.