# How to choose an interpolation method for seismic ground motion signals

I am working with seismic ground motion records from the PEER database. They are acceleration measurements that are band limited to 50 Hz and sampled at 200 Hz.

I use these records to drive an explicit finite element analysis of a structure to determine its response under the earthquake. This analysis runs with a 1e-5 time step (100,000 Hz). If I were to input the sampled records directly the FEA program would linearly interpolate the time steps between the samples, which would distort the signal.

Therefore I need to reconstruct the original signal and resample it at 100,000 Hz (or high enough that the interpolation doesn't affect accuracy much).

One property that I would like to preserve is the double integral of the signal, which gives displacement. This keeps the structure from drifting away over time. I do not care about the calculation time, as it only needs to be done once and is trivial compared to the FEA calculation time.

A previous answer discussed several methods for interpolation but not how to choose from among them.

I have experimented with sinc interpolation using a Kaiser window with an artificially generated signal that I sampled and then reconstructed and I see decent results, but there are visible differences in the time domain.

Is there some way to determine what interpolation method (and parameters in the case of a windowed method) would give the most accurate results?

• If you don't care about calculation time, and you have a large number of samples, sinc interpolation (which is theoretically perfect) should be your choice.
– MBaz
Commented Feb 15, 2017 at 18:22
• @MBaz so by that do you mean sinc interpolation without windowing? Commented Feb 15, 2017 at 21:19
• Yes. Note that in practice you need to truncate the sinc pulse, since it becomes numerically very tricky to handle when the sidelobe amplitudes are small; you may need to experiment. Also, I'm no expert in this area -- you should test this idea and verify it meets your requirements.
– MBaz
Commented Feb 15, 2017 at 22:37