.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "emd_tutorials/00_quick_start/emd_tutorial_00_start_01_quicksift.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_emd_tutorials_00_quick_start_emd_tutorial_00_start_01_quicksift.py>`
        to download the full example code

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

.. _sphx_glr_emd_tutorials_00_quick_start_emd_tutorial_00_start_01_quicksift.py:


Quick-Start: Running a simple EMD
=================================
This getting started tutorial shows how to use EMD to analyse a synthetic signal.

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Running an EMD and frequency transform
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
First of all, we import both the numpy and EMD modules:

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.. code-block:: Python


    # sphinx_gallery_thumbnail_number = 2

    import matplotlib.pyplot as plt
    import numpy as np
    import emd








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We then define a simulated waveform containing a non-linear wave at 5Hz and a sinusoid at 1Hz:

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.. code-block:: Python


    sample_rate = 1000
    seconds = 10
    num_samples = sample_rate*seconds

    time_vect = np.linspace(0, seconds, num_samples)

    freq = 5

    # Change extent of deformation from sinusoidal shape [-1 to 1]
    nonlinearity_deg = 0.25

    # Change left-right skew of deformation [-pi to pi]
    nonlinearity_phi = -np.pi/4

    # Compute the signal

    # Create a non-linear oscillation
    x = emd.simulate.abreu2010(freq, nonlinearity_deg, nonlinearity_phi, sample_rate, seconds)

    x += np.cos(2 * np.pi * 1 * time_vect)        # Add a simple 1Hz sinusoid
    x -= np.sin(2 * np.pi * 2.2e-1 * time_vect)   # Add part of a very slow cycle as a trend

    # Visualise the time-series for analysis
    plt.figure(figsize=(12, 4))
    plt.plot(x)




.. image-sg:: /emd_tutorials/00_quick_start/images/sphx_glr_emd_tutorial_00_start_01_quicksift_001.png
   :alt: emd tutorial 00 start 01 quicksift
   :srcset: /emd_tutorials/00_quick_start/images/sphx_glr_emd_tutorial_00_start_01_quicksift_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    [<matplotlib.lines.Line2D object at 0x7f0ec7ba3d90>]



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Try changing the values of ``nonlinearity_deg`` and ``nonlinearity_phi`` to
create different non-sinusoidal waveform shapes.

Next, we can then estimate the IMFs for the signal:

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.. code-block:: Python


    imf = emd.sift.sift(x)
    print(imf.shape)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    (10000, 4)




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and, from the IMFs, compute the instantaneous frequency, phase and amplitude
using the Normalised Hilbert Transform Method:

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.. code-block:: Python


    IP, IF, IA = emd.spectra.frequency_transform(imf, sample_rate, 'hilbert')








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From the instantaneous frequency and amplitude, we can compute the Hilbert-Huang spectrum:

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.. code-block:: Python


    # Define frequency range (low_freq, high_freq, nsteps, spacing)
    freq_range = (0.1, 10, 80, 'log')
    f, hht = emd.spectra.hilberthuang(IF, IA, freq_range, sum_time=False)








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Visualising the results
^^^^^^^^^^^^^^^^^^^^^^^

we can now plot some summary information, first the IMFs:

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.. code-block:: Python


    emd.plotting.plot_imfs(imf)




.. image-sg:: /emd_tutorials/00_quick_start/images/sphx_glr_emd_tutorial_00_start_01_quicksift_002.png
   :alt: emd tutorial 00 start 01 quicksift
   :srcset: /emd_tutorials/00_quick_start/images/sphx_glr_emd_tutorial_00_start_01_quicksift_002.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <Axes: xlabel='Time (samples)'>



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and now the Hilbert-Huang transform of this decomposition

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.. code-block:: Python


    fig = plt.figure(figsize=(10, 6))
    emd.plotting.plot_hilberthuang(hht, time_vect, f,
                                   time_lims=(2, 4), freq_lims=(0.1, 15),
                                   fig=fig, log_y=True)



.. image-sg:: /emd_tutorials/00_quick_start/images/sphx_glr_emd_tutorial_00_start_01_quicksift_003.png
   :alt: Hilbert-Huang Transform
   :srcset: /emd_tutorials/00_quick_start/images/sphx_glr_emd_tutorial_00_start_01_quicksift_003.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <Axes: title={'center': 'Hilbert-Huang Transform'}, xlabel='Time', ylabel='Frequency'>




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

   **Total running time of the script:** (0 minutes 1.581 seconds)


.. _sphx_glr_download_emd_tutorials_00_quick_start_emd_tutorial_00_start_01_quicksift.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: emd_tutorial_00_start_01_quicksift.ipynb <emd_tutorial_00_start_01_quicksift.ipynb>`

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

      :download:`Download Python source code: emd_tutorial_00_start_01_quicksift.py <emd_tutorial_00_start_01_quicksift.py>`


.. only:: html

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

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