There is a need in certain analysis problems to correct an acceleration signal so that its integrated velocity and double integrated displacement each oscillates about its respective zero baseline. This may require using high pass filtering, trend removal and tapering throughout the integration process. Trial-and-error is required to select the optimum combination of steps.
The steps are needed in part because the initial velocity and displacement are undefined. Also, the acceleration may have a spurious offset or trend for the case of measured data.
Furthermore, the resulting displacement should be such that it can be recovered if it is then double differentiated to acceleration and the acceleration is then double integrated back to displacement. This requirement is for rigor. It yields a consistent set of acceleration, velocity and displacement time histories where each oscillates about its respective zero baseline.
This feature is now included in:
Matlab script: Vibrationdata Signal Analysis Package
Time History > Integrate or Differentiate > Correct Acceleration, Velocity, Displacement
– Tom Irvine