In order to apply the calibration parameters kappas to h(t), we need to low pass it so that the noise (high frequency variation) picked up from the detector is smoothed out and only the low frequency variation, which we are confident is an actual change in the response of IFO, is applied to the data.

The value of kappas (data) obtained from the GDS pipeline is calculated by doing a 10s FFT and stored at 16 Hz to the frame. In order to determine an appropriate low pass filter, I averaged the 16 Hz data at 64s, 128s and 256s. 

The attachment below contains 3 pages of plots for each IFO. I took a day worth of data where there were several locks during the day. The plot on page 1 and 2 are plots for kappa_C and kappa_tst respectively. Each page contains four plots of which the first one is the actual 16 Hz data  with 64s, 128s and 256s averaged data overlayed on top of it. The rest three plot are individual averaged plots.

The plot on the last page is standard deviation of the data after applying the averaging plotted along with the estimate standard deviation as if the variation improved as square root of N. The two agree very closely. This just says that data is normally distributed (could be noise but not necessarily) and variation improves as a square root of average time.