In situ observations of the flanks of the magnetospheric boundary (magnetopause and boundary layer) sometimes show periodic surface waves to be present. We propose a straightforward but powerful technique for analyzing such periodic boundary waves. The result of this analysis is a two-dimensional picture of the structure of the wave in a reference frame that travels tailward with the wave. We give a few examples of wave patterns that can be recovered from AMPTE/IRM data. We demonstrate that the proposed method is a valuable tool that can shed a new light on issues such as the value of the wave speed, the location of flow vortices in the boundary layer, the identification of the unstable surface in the case of a Kelvin-Helmholtz instability, and the non-sinusoidal form of surface waves.