.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/frequencyseries/rayleigh.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_frequencyseries_rayleigh.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_frequencyseries_rayleigh.py:


.. sectionauthor:: Duncan Macleod <duncan.macleod@ligo.org>
.. currentmodule:: gwpy.timeseries

Plotting a Rayleigh-statistic `Spectrum`
########################################

In LIGO the 'Rayleigh' statistic is a calculation of the
`coefficient of variation
<https://en.wikipedia.org/wiki/Coefficient_of_variation>`_ of the
power spectral density (PSD) of a given set of data.
It is used to measure the 'Gaussianity' of those data, where a value of 1
indicates Gaussian behaviour, less than 1 indicates coherent variations,
and greater than 1 indicates incoherent variation.
It is a useful measure of the quality of the strain data being generated
and recorded at a LIGO site.

.. GENERATED FROM PYTHON SOURCE LINES 38-40

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

.. GENERATED FROM PYTHON SOURCE LINES 40-48

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 49-52

Next, we can calculate a Rayleigh statistic `FrequencySeries` using the
:meth:`~gwpy.timeseries.TimeSeries.rayleigh_spectrum` method of the
`~gwpy.timeseries.TimeSeries` with a 2-second FFT and 1-second overlap (50%):

.. GENERATED FROM PYTHON SOURCE LINES 52-55

.. code-block:: Python


    rayleigh = gwdata.rayleigh_spectrum(2, 1)








.. GENERATED FROM PYTHON SOURCE LINES 56-58

For easy comparison, we can calculate the spectral sensitivity ASD of the
strain data and plot both on the same figure:

.. GENERATED FROM PYTHON SOURCE LINES 58-79

.. code-block:: Python


    from gwpy.plot import Plot
    plot = Plot(
        gwdata.asd(2, 1),
        rayleigh,
        geometry=(2, 1),
        sharex=True,
        xscale="log",
        xlim=(30, 1500),
    )
    asdax, rayax = plot.axes
    # update ASD Axes
    asdax.set_title("Sensitivity of LIGO-Livingston around GW151226")
    asdax.set_yscale("log")
    asdax.set_ylim(5e-24, 1e-21)
    asdax.set_ylabel(r"[strain/$\sqrt{\mathrm{Hz}}$]")
    # update Rayleigh Axes
    rayax.set_ylim(0, 2)
    rayax.set_ylabel("Rayleigh statistic")
    plot.show()




.. image-sg:: /examples/frequencyseries/images/sphx_glr_rayleigh_001.png
   :alt: Sensitivity of LIGO-Livingston around GW151226
   :srcset: /examples/frequencyseries/images/sphx_glr_rayleigh_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 80-84

So, we see sharp dips at certain frequencies associated with 'lines' in
spectrum where noise at a fixed frequency is very coherent (e.g. harmonics
of the 60Hz mains power supply), and bumps in specific frequency bands
where the interferometer noise is non-stationary.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 1.794 seconds)


.. _sphx_glr_download_examples_frequencyseries_rayleigh.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: rayleigh.ipynb <rayleigh.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: rayleigh.py <rayleigh.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: rayleigh.zip <rayleigh.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_