2. Compute the raw Q-transform of a
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
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).
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, )
To recover as much signal as possible, in practice we should suppress
background noise by whitening the data before the Q-transform. This
can be done with
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()
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.