Whitening a TimeSeries

Most data recorded from a gravitational-wave interferometer carry information across a wide band of frequencies, typically up to a few kiloHertz, but often it is the case that the low-frequency amplitude dwarfs that of the high-frequency content, making discerning high-frequency features difficult. This is especially true of the LIGO differential arm strain measurement, which encodes any gravitational wave signals that are present.

We employ a technique called ‘whitening’ to normalize the power at all frequencies so that excess power at any frequency is more obvious.

We demonstrate below the LIGO-Livingston gravitational-wave strain measurement signal around GW200129, the loudest signal as yet detected by LIGO.

Data access

First, we use the gwosc Python client to get the GPS time of the event:

from gwosc.datasets import event_gps
gps = event_gps("GW200129_065458")

Then we can import the TimeSeries object and fetch the strain data using TimeSeries.fetch_open_data() in a window around that event:

from gwpy.timeseries import TimeSeries
data = TimeSeries.fetch_open_data("L1", int(gps) - 64, int(gps) + 64)

To demonstrate the relative power across the frequency band, we can quickly estimate an Amplitude Spectral Density (ASD) for these data:

asd = data.asd(fftlength=8)
plot = asd.plot(
    xlim=(8, 1000),
    ylabel="Strain ASD [$1/\\sqrt{Hz}$]",
)
plot.show()

Whitening

The ASD clearly shows the dominance in amplitude of the lowest frequency components of the data, where the seismic noise around the observatory is most impactful. We can now whiten() the data to to normalise the amplitudes across the frequency range:

white = data.whiten(fftlength=8)

and can plot both the original and whitened data around the event time:

from gwpy.plot import Plot
plot = Plot(
    data,
    white,
    separate=True,
    sharex=True,
    epoch=gps,
    xlim=(gps - 1, gps + 1),
)
plot.axes[0].set_ylabel("Strain amplitude", fontsize=16)
plot.axes[1].set_ylabel("Whitened strain amplitude", fontsize=16)
plot.show()

The top figure is dominated by the low-frequency noise, whereas the whitened data below highlights a few spikes in the data at higher frequencies.

We can zoom in very close around the event time:

plot = white.crop(gps - .1, gps + .1).plot(
    ylabel="Whitened strain amplitude",
)
plot.axes[0].set_epoch(gps)
plot.show()

Here, centred around time 0.03 is the clear signature of a binary black hole merger, GW200129. This signal is completely hidden in the unfiltered data, but the simple act of whitening has exposed the loudest gravitational-wave event ever detected!