The surface roughness of evaporated gold films has been studied by scanning tunneling microscopy and a frequency analysis method that uses the whole image. The power spectrum $\mathbf{S}(q,t)$ presents a clear ${q}^{\ensuremath{-}\ensuremath{\gamma}}$ dependence in the region of high frequencies and the interface width of the films follows a ${t}^{\ensuremath{\beta}}$ behavior. The values obtained for the two exponents $(\ensuremath{\gamma}=4.1$ and $\ensuremath{\beta}=0.26)$ agree with the theoretical predictions $(\ensuremath{\gamma}=4$ and $\ensuremath{\beta}=0.25)$ for a process controlled by pure surface diffusion in the thickness range studied. The power spectrum at high frequencies is similar for different film thickness describing a phenomenon free from anomalous scaling. We also conclude that dimensional analysis of profiles presents some practical problems in its application. On the other hand, frequency analysis of the whole image allows us to obtain a reliable determination of surface roughness.