Retrieving the time history of displacement from measured acceleration signal

It is intended to retrieve the time history of displacement from measured acceleration signal. In this study, the word retrieving means reconstructing the time history of original displacement signal from already measured acceleration signal not just extracting various information using relevant signal processing techniques. Unlike extracting required information from the signal, there are not many options to apply to retrieve the time history of displacement signal, once the acceleration signal is measured and recorded with given sampling rate. There are two methods, in general, to convert measured acceleration signal into displacement signal. One is directly integrating the acceleration signal in time domain. The other is dividing the Fourier transformed acceleration signal by the scale factor of -ω² and taking the inverse Fourier transform of it. It turned out both the methods produced a significant amount of errors depending on the sampling resolution in time and frequency domain when digitizing the acceleration signals. A simple and effective way to convert the time history of acceleration signal into the time history of displacement signal without significant errors is studied here with the analysis on the errors involved in the conversion process.