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

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

.. _sphx_glr_auto_examples_plot_time_frequency.py:


Hilbert spectrum and Morlet wavelets on a chirp
===============================================

A tone that sweeps from 0.02 to 0.2 Hz. The Hilbert spectrum of its MVMD modes follows the sweep
sample by sample; the Morlet CWT smooths it over each wavelet's length and marks where edge
effects make values unreliable (the cone of influence).

.. GENERATED FROM PYTHON SOURCE LINES 9-34



.. image-sg:: /auto_examples/images/sphx_glr_plot_time_frequency_001.png
   :alt: Hilbert spectrum of the MVMD mode, Morlet CWT, outside the cone of influence
   :srcset: /auto_examples/images/sphx_glr_plot_time_frequency_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    import modewise

    fs = 1.25
    t = np.arange(800) / fs
    phase = 2 * np.pi * (0.02 * t + 0.5 * (0.18 / t[-1]) * t**2)
    x = np.vstack([np.sin(phase)])

    modes = modewise.mvmd(x, fs, num_modes=1, alpha=50.0)
    hilbert = modewise.hilbert_spectrum(modewise.hilbert(modes), 0.01, 0.3, 60)
    cwt = modewise.cwt(x, fs, 0.01, 0.3, 60)

    fig, (a, b) = plt.subplots(2, 1, figsize=(9, 6), sharex=True)
    a.pcolormesh(t, hilbert.frequencies_hz, hilbert.power[0], shading="auto")
    a.set_title("Hilbert spectrum of the MVMD mode")
    b.pcolormesh(t, cwt.frequencies_hz, np.where(cwt.reliable, cwt.power[0], np.nan), shading="auto")
    b.set_title("Morlet CWT, outside the cone of influence")
    for ax in (a, b):
        ax.plot(t, 0.02 + (0.18 / t[-1]) * t, "w--", lw=0.8)
        ax.set_ylabel("frequency (Hz)")
    b.set_xlabel("time (s)")
    fig.tight_layout()


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

   **Total running time of the script:** (0 minutes 0.119 seconds)


.. _sphx_glr_download_auto_examples_plot_time_frequency.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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