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

.. only:: html

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

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

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

.. _sphx_glr_examples_fourier_transform.py:


Fourier transform
=================

The graph Fourier transform :meth:`pygsp.graphs.Graph.gft` transforms a
signal from the vertex domain to the spectral domain. The smoother the signal
(see :meth:`pygsp.graphs.Graph.dirichlet_energy`), the lower in the frequencies
its energy is concentrated.

.. GENERATED FROM PYTHON SOURCE LINES 10-48



.. image-sg:: /examples/images/sphx_glr_fourier_transform_001.png
   :alt: $x^T L x = 0.30$, $x^T L x = 1.55$, $x^T L x = 5.43$
   :srcset: /examples/images/sphx_glr_fourier_transform_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import numpy as np
    from matplotlib import pyplot as plt

    import pygsp as pg

    G = pg.graphs.Sensor(seed=42)
    G.compute_fourier_basis()

    scales = [10, 3, 0]
    limit = 0.44

    fig, axes = plt.subplots(2, len(scales), figsize=(12, 4))
    fig.subplots_adjust(hspace=0.5)

    x0 = np.random.default_rng(1).normal(size=G.N)
    for i, scale in enumerate(scales):
        g = pg.filters.Heat(G, scale)
        x = g.filter(x0).squeeze()
        x /= np.linalg.norm(x)
        x_hat = G.gft(x).squeeze()

        assert np.all((-limit < x) & (x < limit))
        G.plot(x, limits=[-limit, limit], ax=axes[0, i])
        axes[0, i].set_axis_off()
        axes[0, i].set_title(f"$x^T L x = {G.dirichlet_energy(x):.2f}$")

        axes[1, i].plot(G.e, np.abs(x_hat), ".-")
        axes[1, i].set_xticks(range(0, 16, 4))
        axes[1, i].set_xlabel(r"graph frequency $\lambda$")
        axes[1, i].set_ylim(-0.05, 0.95)

    axes[1, 0].set_ylabel(r"frequency content $\hat{x}(\lambda)$")

    # axes[0, 0].set_title(r'$x$: signal in the vertex domain')
    # axes[1, 0].set_title(r'$\hat{x}$: signal in the spectral domain')

    fig.tight_layout()


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

   **Total running time of the script:** (0 minutes 0.458 seconds)

**Estimated memory usage:**  160 MB


.. _sphx_glr_download_examples_fourier_transform.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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