# 5. Plotting a `Spectrogram`

of the Rayleigh statistic¶

As described in Plotting a Rayleigh-statistic Spectrum, the Rayleigh statistic can be used to study non-Gaussianity in a timeseries. We can study the time variance of these features by plotting a time-frequency spectrogram where we calculate the Rayleigh statistic for each time bin.

To demonstate this, we can load some data from the LIGO Livingston intereferometer around the time of the GW151226 gravitational wave detection:

```
from gwpy.timeseries import TimeSeries
gwdata = TimeSeries.fetch_open_data('L1', 'Dec 26 2015 03:37',
'Dec 26 2015 03:47', verbose=True)
```

Next, we can calculate a Rayleigh statistic `Spectrogram`

using the
`rayleigh_spectrogram()`

method of the
`TimeSeries`

and a 5-second stride with a 2-second FFT and
1-second overlap (50%):

```
rayleigh = gwdata.rayleigh_spectrogram(5, fftlength=2, overlap=1)
```

and can make a plot using the `plot()`

method

```
plot = rayleigh.plot(norm='log', vmin=0.25, vmax=4)
ax = plot.gca()
ax.set_yscale('log')
ax.set_ylim(30, 1500)
ax.set_title('Sensitivity of LIGO-Livingston around GW151226')
ax.colorbar(cmap='coolwarm', label='Rayleigh statistic')
plot.show()
```

(`png`

)