FFT integration of time series using an overlap-add technique

Abstract

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. The idea is to perform the integration in the frequency domain dividing the Fourier Transform by 2πif, and then transforming back to time domain by IFFT. The technique is implemented using an overlap-add finite data segment approach, and the drift problem is solved by forcing the DC value of the frequency domain representation of the integrated signal to zero. ©2010 Society for Experimental Mechanics Inc.