Transfer function

In this example we demonstrate how to calculate the transfer function between two TimeSeries signals.

All ground-based gravitational wave observatories would be unable to operate if they did not employ sophisticated ground-motion suppression technology to prevent vibrations from the local (or remote) environment from transferring through to optical components.

The impact of the seismic isolation system can be seen by calculating the transfer function between the ground motion at the laboratory and that of the optical suspension points.

from gwpy.time import tconvert
from gwpy.timeseries import TimeSeriesDict
from gwpy.plot import BodePlot

For this example we will use data from the Auxiliary Channel Three Hour Release:

start = tconvert("August 14 2017 10:25")
end = start + 1800
gndchannel = "L1:ISI-GND_STS_ITMY_Y_DQ"
suschannel = "L1:ISI-ITMY_SUSPOINT_ITMY_EUL_L_DQ"

We can call the get() method of the TimeSeriesDict to retrieve all data in a single operation:

data = TimeSeriesDict.get(
    [gndchannel, suschannel],
    start,
    end,
    verbose=True,
    host="nds.gwosc.org",
)
gnd = data[gndchannel]
sus = data[suschannel]

- Attempting data access from files
Cannot locate the following channel(s) in any known frametype at GPS=1186741518:
    L1:ISI-ITMY_SUSPOINT_ITMY_EUL_L_DQ
    L1:ISI-GND_STS_ITMY_Y_DQ
[files on tape have not been checked, use allow_tape=True for a complete search]
Data access from files failed
- Attempting data access from NDS2

The transfer function between time series is easily computed with the transfer_function() method:

tf = gnd.transfer_function(sus, fftlength=128, overlap=64)

The BodePlot knows how to separate a complex-valued FrequencySeries into magnitude and phase:

plot = BodePlot(tf)
plot.maxes.set_title(
    r"L1 ITMY ground $\rightarrow$ SUS transfer function",
)
plot.maxes.set_xlim(5e-2, 30)
plot.show()

# This example demonstrates the impressive noise suppression of the LIGO
# seismic isolation system. For more details, please see
# https://www.ligo.caltech.edu/page/vibration-isolation.