.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_decompositions.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_plot_decompositions.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_decompositions.py:


Three ways to split a signal into modes
=======================================

A slow (0.02 Hz) and a fast (0.18 Hz) rhythm on a drift, decomposed by MVMD, EMD and the MODWT
multiresolution analysis.

- MVMD finds the number of modes you ask for, at frequencies it adapts to the data.
- EMD finds as many oscillations as the data hold, with the drift as its residual (mode 0). It
  also pulls two weak slow modes out of the drift and the edges, a known EMD behaviour.
- The MODWT splits into fixed octaves. The 0.02 Hz tone sits at the edge between two octaves at
  this sampling rate, so the smooth and D5 share it.

EMD and the MODWT add back up to the signal exactly; MVMD with ``tau = 0`` leaves out what does not
fit its modes.

.. GENERATED FROM PYTHON SOURCE LINES 17-46



.. image-sg:: /auto_examples/images/sphx_glr_plot_decompositions_001.png
   :alt: MVMD (K = 3), EMD, MODWT MRA (sym4, 5 levels)
   :srcset: /auto_examples/images/sphx_glr_plot_decompositions_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    MVMD (K = 3): 3 modes, largest reconstruction error 2.68e-01
    EMD: 5 modes, largest reconstruction error 4.44e-16
    MODWT MRA (sym4, 5 levels): 6 modes, largest reconstruction error 2.69e-12






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    import modewise

    fs = 1.25
    t = np.arange(600) / fs
    x = np.vstack([np.sin(2 * np.pi * 0.02 * t) + 0.6 * np.sin(2 * np.pi * 0.18 * t) + 0.004 * t])

    results = {
        "MVMD (K = 3)": modewise.mvmd(x, fs, num_modes=3, alpha=2000.0, init="linear", tau=0.0),
        "EMD": modewise.emd(x, fs),
        "MODWT MRA (sym4, 5 levels)": modewise.modwt_mra(x, fs, levels=5, boundary="reflection"),
    }

    fig, axes = plt.subplots(1, 3, figsize=(12, 5), sharex=True)
    for ax, (name, d) in zip(axes, results.items()):
        for k in range(d.n_modes):
            ax.plot(t, d.modes[k, 0] - 2.5 * k, lw=0.8)
            ax.text(t[-1] + 5, -2.5 * k, f"{d.centre_frequencies_hz[k]:.3f} Hz", va="center", fontsize=7)
        ax.set_title(name, fontsize=10)
        ax.set_yticks([])
        ax.set_xlabel("time (s)")
    fig.tight_layout()

    for name, d in results.items():
        error = np.abs(d.modes.sum(axis=0) - x).max()
        print(f"{name}: {d.n_modes} modes, largest reconstruction error {error:.2e}")


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

   **Total running time of the script:** (0 minutes 0.084 seconds)


.. _sphx_glr_download_auto_examples_plot_decompositions.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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