.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery_2d/plot_filters.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_gallery_2d_plot_filters.py>`
        to download the full example code

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

.. _sphx_glr_gallery_2d_plot_filters.py:


Plot the 2D wavelet filters
===========================
See :meth:`kymatio.scattering2d.filter_bank` for more informations about the used wavelets.

.. GENERATED FROM PYTHON SOURCE LINES 6-14

.. code-block:: default


    from colorsys import hls_to_rgb
    import matplotlib.pyplot as plt
    import numpy as np
    from kymatio.scattering2d.filter_bank import filter_bank
    from scipy.fft import fft2









.. GENERATED FROM PYTHON SOURCE LINES 15-17

Initial parameters of the filter bank
-------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 17-22

.. code-block:: default

    M = 32
    J = 3
    L = 8
    filters_set = filter_bank(M, M, J, L=L)








.. GENERATED FROM PYTHON SOURCE LINES 23-26

Imshow complex images
---------------------
Thanks to https://stackoverflow.com/questions/17044052/mathplotlib-imshow-complex-2d-array

.. GENERATED FROM PYTHON SOURCE LINES 26-41

.. code-block:: default



    def colorize(z):
        n, m = z.shape
        c = np.zeros((n, m, 3))
        c[np.isinf(z)] = (1.0, 1.0, 1.0)
        c[np.isnan(z)] = (0.5, 0.5, 0.5)

        idx = ~(np.isinf(z) + np.isnan(z))
        A = (np.angle(z[idx]) + np.pi) / (2*np.pi)
        A = (A + 0.5) % 1.0
        B = 1.0/(1.0 + abs(z[idx])**0.3)
        c[idx] = [hls_to_rgb(a, b, 0.8) for a, b in zip(A, B)]
        return c








.. GENERATED FROM PYTHON SOURCE LINES 42-45

Bandpass filters
----------------
First, we display each wavelet according to its scale and orientation.

.. GENERATED FROM PYTHON SOURCE LINES 45-66

.. code-block:: default

    fig, axs = plt.subplots(J, L, sharex=True, sharey=True)
    fig.set_figheight(6)
    fig.set_figwidth(6)
    plt.rc('text', usetex=True)
    plt.rc('font', family='serif')
    i = 0
    for filter in filters_set['psi']:
        f = filter["levels"][0]
        filter_c = fft2(f)
        filter_c = np.fft.fftshift(filter_c)
        axs[i // L, i % L].imshow(colorize(filter_c))
        axs[i // L, i % L].axis('off')
        axs[i // L, i % L].set_title(
            "$j = {}$ \n $\\theta={}$".format(i // L, i % L))
        i = i+1

    fig.suptitle((r"Wavelets for each scales $j$ and angles $\theta$ used."
                  "\nColor saturation and color hue respectively denote complex "
                  "magnitude and complex phase."), fontsize=13)
    fig.show()




.. image-sg:: /gallery_2d/images/sphx_glr_plot_filters_001.png
   :alt: Wavelets for each scales $j$ and angles $\theta$ used. Color saturation and color hue respectively denote complex magnitude and complex phase., $j = 0$   $\theta=0$, $j = 0$   $\theta=1$, $j = 0$   $\theta=2$, $j = 0$   $\theta=3$, $j = 0$   $\theta=4$, $j = 0$   $\theta=5$, $j = 0$   $\theta=6$, $j = 0$   $\theta=7$, $j = 1$   $\theta=0$, $j = 1$   $\theta=1$, $j = 1$   $\theta=2$, $j = 1$   $\theta=3$, $j = 1$   $\theta=4$, $j = 1$   $\theta=5$, $j = 1$   $\theta=6$, $j = 1$   $\theta=7$, $j = 2$   $\theta=0$, $j = 2$   $\theta=1$, $j = 2$   $\theta=2$, $j = 2$   $\theta=3$, $j = 2$   $\theta=4$, $j = 2$   $\theta=5$, $j = 2$   $\theta=6$, $j = 2$   $\theta=7$
   :srcset: /gallery_2d/images/sphx_glr_plot_filters_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 67-70

Lowpass filter
--------------
We finally display the low-pass filter.

.. GENERATED FROM PYTHON SOURCE LINES 70-87

.. code-block:: default

    plt.figure()
    plt.rc('text', usetex=True)
    plt.rc('font', family='serif')
    plt.axis('off')
    plt.set_cmap('gray_r')

    f = filters_set['phi']["levels"][0]

    filter_c = fft2(f)
    filter_c = np.fft.fftshift(filter_c)
    plt.suptitle(("The corresponding low-pass filter, also known as scaling "
                  "function.\nColor saturation and color hue respectively denote "
                  "complex magnitude and complex phase"), fontsize=13)
    filter_c = np.abs(filter_c)
    plt.imshow(filter_c)

    plt.show()



.. image-sg:: /gallery_2d/images/sphx_glr_plot_filters_002.png
   :alt: The corresponding low-pass filter, also known as scaling function. Color saturation and color hue respectively denote complex magnitude and complex phase
   :srcset: /gallery_2d/images/sphx_glr_plot_filters_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  2.355 seconds)


.. _sphx_glr_download_gallery_2d_plot_filters.py:

.. only:: html

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


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

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

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

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


.. only:: html

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

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