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

    Click :ref:`here <sphx_glr_download_auto_examples_plot_4_2_2_bertrand_hyperbolic_gd.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_plot_4_2_2_bertrand_hyperbolic_gd.py:


========================================================
Bertrand Distribution of a Hyperbolic Group Delay Signal
========================================================

This example shows the Bertrand distribution of a signal with hyperbolic group
delay. The distribution is well localized around the hyperbola, but not
perfectly. The Bertrand distribution operates only on a part of the frequency
range between two bounds :math:`f_{min}` and :math:`f_{max}`.

Figure 4.21 from the tutorial.



.. image:: /auto_examples/images/sphx_glr_plot_4_2_2_bertrand_hyperbolic_gd_001.png
    :class: sphx-glr-single-img





.. code-block:: default


    from tftb.processing.affine import BertrandDistribution
    from tftb.generators import gdpower


    sig = gdpower(128)[0]
    bert = BertrandDistribution(sig, fmin=0.01, fmax=0.22)
    bert.run()
    bert.plot()


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

   **Total running time of the script:** ( 0 minutes  0.967 seconds)


.. _sphx_glr_download_auto_examples_plot_4_2_2_bertrand_hyperbolic_gd.py:


.. only :: html

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



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_4_2_2_bertrand_hyperbolic_gd.py <plot_4_2_2_bertrand_hyperbolic_gd.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_4_2_2_bertrand_hyperbolic_gd.ipynb <plot_4_2_2_bertrand_hyperbolic_gd.ipynb>`


.. only:: html

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

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