2. Compute the raw Q-transform of a TimeSeries¶

One of the most useful tools for visualising short-duration features in a TimeSeries is the Q-transform. This tool is routinely used by data analysts to produce time-frequency maps of both transient noise (glitches) and astrophysical signals from ground-based gravitational-wave detectors.

Below we use this algorithm to visualise GW170817, a gravitational-wave signal from two merging neutron stars. In the LIGO-Livingston (L1) detector, the end of this signal coincides with a very loud glitch (Phys. Rev. Lett. vol. 119, p. 161101).

First, we need to download the TimeSeries record of L1 strain measurements from GWOSC:

from gwosc import datasets
from gwpy.timeseries import TimeSeries
gps = datasets.event_gps('GW170817')
data = TimeSeries.fetch_open_data('L1', gps-34, gps+34)

We can Q-transform these data and scan over time-frequency planes to find the one with the most significant tile near the time of merger:

from gwpy.segments import Segment
qgram = data.q_gram(
    qrange=(4, 150),
    search=Segment(gps-0.25, gps+0.25),
    mismatch=0.35,
)

Finally, we can plot the loudest time-frequency plane, focusing on a specific window around the merger time:

plot = qgram.tile(
    'time',
    'frequency',
    'duration',
    'bandwidth',
    color='energy',
)
ax = plot.gca()
ax.set_xscale('seconds')
ax.set_xlim(gps-6, gps+1)
ax.set_epoch(gps)
ax.set_yscale('log')
ax.set_ylim(16, 1024)
ax.set_ylabel('Frequency [Hz]')
ax.grid(True, axis='y', which='both')
from matplotlib import colormaps
cmap = colormaps['viridis']
ax.colorbar(cmap=cmap.name, label='Normalized energy', clim=[0, 50])
ax.set_facecolor(cmap(0))  # colour background to the bottom of the map
plot.show()

(png)

Here we can clearly see the trace of a binary neutron star merger, sweeping up in frequency through a loud saturation glitch in the foreground. For more details on this result, please see the ‘Science Summary’ for GW170817.