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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_example_echt.py:


Endpoint-corrected Hilbert transform (ECHT) phase estimation
============================================================

This example shows how to causally estimate the phase of a signal using the
Endpoint-corrected Hilbert transform (ECHT) [1]_.

Uses `meegkit.phase.ECHT()`.

References
----------
.. [1] Schreglmann, S. R., Wang, D., Peach, R. L., Li, J., Zhang, X., Latorre,
    A., ... & Grossman, N. (2021). Non-invasive suppression of essential tremor
    via phase-locked disruption of its temporal coherence. Nature
    communications, 12(1), 363.

.. GENERATED FROM PYTHON SOURCE LINES 18-29

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np
    from scipy.signal import hilbert

    from meegkit.phase import ECHT

    rng = np.random.default_rng(38872)

    plt.rcParams["axes.grid"] = True
    plt.rcParams["grid.linestyle"] = ":"








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Build data
-----------------------------------------------------------------------------
First, we generate a multi-component signal with amplitude and phase
modulations, as described in the paper [1]_.

.. GENERATED FROM PYTHON SOURCE LINES 34-43

.. code-block:: Python

    f0 = 2

    N = 500
    sfreq = 100
    time = np.linspace(0, N / sfreq, N)
    X = np.cos(2 * np.pi * f0 * time - np.pi / 4)
    phase_true = np.angle(hilbert(X))
    X += rng.normal(0, 0.5, N)  # Add noise








.. GENERATED FROM PYTHON SOURCE LINES 44-48

Compute phase and amplitude
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We compute the Hilbert phase, as well as the phase obtained with the ECHT
filter.

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.. code-block:: Python

    phase_hilbert = np.angle(hilbert(X))  # Hilbert phase

    # Compute ECHT-filtered signal
    filt_BW = f0 / 2
    l_freq = f0 - filt_BW / 2
    h_freq = f0 + filt_BW / 2
    echt = ECHT(l_freq, h_freq, sfreq)

    Xf = echt.fit_transform(X)
    phase_echt = np.angle(Xf)








.. GENERATED FROM PYTHON SOURCE LINES 60-65

Visualize signal
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Here we plot the original signal, its Fourier spectrum, and the phase obtained
with the Hilbert transform and the ECHT filter. The ECHT filter provides a
much smoother phase estimate than the Hilbert transform

.. GENERATED FROM PYTHON SOURCE LINES 65-82

.. code-block:: Python

    fig, ax = plt.subplots(3, 1, figsize=(8, 6))
    ax[0].plot(time, X)
    ax[0].set_xlabel("Time (s)")
    ax[0].set_title("Test signal")
    ax[0].set_ylabel("Amplitude")
    ax[1].psd(X, Fs=sfreq, NFFT=2048*4, noverlap=sfreq)
    ax[1].set_ylabel("PSD (dB/Hz)")
    ax[1].set_title("Test signal's Fourier spectrum")
    ax[2].plot(time, phase_true, label="True phase", ls=":")
    ax[2].plot(time, phase_echt, label="ECHT phase", lw=.5, alpha=.8)
    ax[2].plot(time, phase_hilbert, label="Hilbert phase", lw=.5, alpha=.8)
    ax[2].set_title("Phase")
    ax[2].set_ylabel("Amplitude")
    ax[2].set_xlabel("Time (s)")
    ax[2].legend(loc="upper right", fontsize="small")
    plt.tight_layout()
    plt.show()



.. image-sg:: /auto_examples/images/sphx_glr_example_echt_001.png
   :alt: Test signal, Test signal's Fourier spectrum, Phase
   :srcset: /auto_examples/images/sphx_glr_example_echt_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.305 seconds)


.. _sphx_glr_download_auto_examples_example_echt.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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