Many times in vibration problems it is of importance to be able to integrate signals. Well known cases are Operational Deflection Shapes and earth quake problems where the displacements often need to be estimated from acceleration time series. When digital signals are integrated some classical problems arise; one of these is numerical noise introduced by the inaccurate integration algorithms resulting in large errors in the low frequency region leading to large DC drift. These problems are normally dealt with by using high pass filters that often introduce additional implementation problems like instability and amplitude/phase distorting problems. In this paper an FFT based procedure is introduced.