Wall pressure measurements may results from two contributions: one coming from the acoustic sources and an- other induced by the turbulent boundary layer (TBL) pressure. An accurate separation of these two contributions may be required for two purposes: first, the extraction of the acoustic part is necessary for the quantification and the localization of the acoustic sources and second, the extraction of the TBL part is needed for the characterization of the vibro-acoustic excitation of the wall. In this paper, a post-processing method is proposed to perform this sep- aration through a decomposition of the measured cross-spectral matrix using the statistical properties of the two contributions, especially their different spatial correlation structures. The approach is assessed on parietal pressure measurements acquired in a wind-tunnel with controlled sources and flow.