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I have a vector containing acceleration measurements and the corresponding vector of times in which measurements are taken.

To obtain velocity and displacement I used the cumtrapz() function already implemented in MATLAB. This should be fine, as I read here Numerical integration of non-uniform acceleration samples and here https://stackoverflow.com/questions/9881430/numerical-integration-using-simpsons-rule-on-discrete-data.

My doubts are related to the disturbances introduced by the integration algorithm as I found in a book a chapter in which the author says that the trapezium rule introduces low-frequency disturbances.

I tried to remove these disturbances and unwanted 0-frequency components (the acceleration was not 0-mean therefore I had a linear trend in the velocity) applying a 2nd order, highpass, butterworht filter with cut-off frequency at 5 Hz (in both directions to null the phase shift) to the velocity and the displacement but I don't know if this is enough or too much because I need very accurate values for velocity and displacement since I have to use them to plot a surface in the state-space (EDIT: phase-space).

How can I choose the correct cut-off frequency in order not to loose any important information knowing that the experimental structure is excited in a range of frequencies from 5 to 100 Hz?

EDIT Since I have to integrate noisy data, is it advisable to use an higher order method if my goal is accuracy?

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  • $\begingroup$ Did you try a higher order method? Something like this? $\endgroup$ – nicoguaro Nov 2 '14 at 2:23
  • $\begingroup$ I tried that method but nothing changed $\endgroup$ – Rhei Nov 2 '14 at 13:47
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    $\begingroup$ I presume from your comments regarding frequencies that the acceleration data is oscillatory? $\endgroup$ – Geoff Oxberry Nov 3 '14 at 21:06
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    $\begingroup$ My acceleration is a measurement of the structure vibration due to a logarithmic sine-sweep base excitation. $\endgroup$ – Rhei Nov 3 '14 at 21:09
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    $\begingroup$ If you have acceleration data and initial conditions for velocity and position, plus knowledge of the allowable frequency range, you might try using a Fourier representation of your acceleration data and integrate that twice in time. $\endgroup$ – Geoff Oxberry Nov 29 '14 at 3:03

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