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

    Click :ref:`here <sphx_glr_download_auto_examples_erpac_plot_erpac.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_erpac_plot_erpac.py:


======================================
Event-Related Phase Amplitude Coupling
======================================

Event-Related Phase-Amplitude Coupling (ERPAC) do not measure PAC across time
cycle but instead, across trials (just as proposed JP. Lachaux with the
PLV/PLS) or with the Inter-Trial Coherence (ITC). Measuring across trials
enable to have a real-time estimation of PAC.

In this example, we generate a signal that have a 10hz phase <->100 hz
amplitude coupling first followed by a random noise.


.. code-block:: default

    import numpy as np

    from tensorpac import EventRelatedPac
    from tensorpac.signals import pac_signals_wavelet

    import matplotlib.pyplot as plt







Generate a synthetic signal
##############################################################################
 in order to illustrate how the ERPAC does works, we are going to concatenate
 two signals. A first one with an alpha <-> gamma coupling during one second
 and then a second one which is going to be a one second random noise


.. code-block:: default


    # First signal consisting of a one second 10 <-> 100hz coupling
    n_epochs = 300
    n_times = 1000
    sf = 1000.
    x1, tvec = pac_signals_wavelet(f_pha=10, f_amp=100, n_epochs=n_epochs, noise=2,
                                   n_times=n_times, sf=sf)

    # Second signal : one second of random noise
    x2 = np.random.rand(n_epochs, 1000)

    # now, concatenate the two signals across the time axis
    x = np.concatenate((x1, x2), axis=1)
    time = np.arange(x.shape[1]) / sf








Define an ERPAC object and extract the phase and the amplitude
##############################################################################
 use :class:`tensorpac.EventRelatedPac.filter` method to extract phases and
 amplitudes


.. code-block:: default


    # define an ERPAC object
    p = EventRelatedPac(f_pha=[9, 11], f_amp='hres')

    # extract phases and amplitudes
    pha = p.filter(sf, x, ftype='phase', n_jobs=1)
    amp = p.filter(sf, x, ftype='amplitude', n_jobs=1)







Compute the ERPAC using the two implemented methods and plot it
##############################################################################


.. code-block:: default


    # implemented ERPAC methods
    methods = ['circular', 'gc']

    plt.figure(figsize=(14, 8))
    for n_m, m in enumerate(methods):
        # compute the erpac
        erpac = p.fit(pha, amp, method=m, smooth=100, n_jobs=-1).squeeze()

        # plot
        plt.subplot(len(methods), 1, n_m + 1)
        p.pacplot(erpac, time, p.yvec, xlabel='Time (second)' * n_m,
                  cmap='Spectral_r', ylabel='Amplitude frequency', title=p.method,
                  cblabel='ERPAC', vmin=0., rmaxis=True)
        plt.axvline(1., linestyle='--', color='w', linewidth=2)

    plt.tight_layout()
    p.show()



.. image:: /auto_examples/erpac/images/sphx_glr_plot_erpac_001.png
    :class: sphx-glr-single-img





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

   **Total running time of the script:** ( 0 minutes  21.963 seconds)


.. _sphx_glr_download_auto_examples_erpac_plot_erpac.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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