I have an acceleration signal sample and I need to get velocity and movement spectrum (amplitudes and phases) from it. I try to solve this problem in two ways:
- First method
- Get FFT of acceleration signal.
- To get velocity amplitudes I divide each acceleration amplitude by $2\pi f$ and subtract $\pi/2$ from each acceleration phase.
- To get the amplitudes of the movement spectrum I divide each acceleration amplitude by $4\pi^2f^2$ and subtract $\pi$ from each acceleration phase.
- Second method
- Using trapezoidal integration, I normalize the acceleration signal.
- I then take an integral of it to get the velocity.
- After this I take the FFT of the velocity.
- I then normalize the velocity and take the integral to get the movement.
- Finally I take the FFT of the movement.
The results obtained with these two methods are slightly different (spectrums amplitudes values). Which method is preferable to use?