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

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

.. _sphx_glr_intro_scipy_auto_examples_solutions_plot_periodicity_finder.py:


==========================
Crude periodicity finding
==========================

Discover the periods in evolution of animal populations
(:download:`../../../../data/populations.txt`)


Load the data
###########################################################



.. code-block:: python


    import numpy as np
    data = np.loadtxt('../../../../data/populations.txt')
    years = data[:, 0]
    populations = data[:, 1:]







Plot the data
###########################################################



.. code-block:: python


    import matplotlib.pyplot as plt
    plt.figure()
    plt.plot(years, populations * 1e-3)
    plt.xlabel('Year')
    plt.ylabel('Population number ($\cdot10^3$)')
    plt.legend(['hare', 'lynx', 'carrot'], loc=1)




.. image:: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_periodicity_finder_001.png
    :class: sphx-glr-single-img




Plot its periods
###########################################################



.. code-block:: python

    from scipy import fftpack

    ft_populations = fftpack.fft(populations, axis=0)
    frequencies = fftpack.fftfreq(populations.shape[0], years[1] - years[0])
    periods = 1 / frequencies

    plt.figure()
    plt.plot(periods, abs(ft_populations) * 1e-3, 'o')
    plt.xlim(0, 22)
    plt.xlabel('Period')
    plt.ylabel('Power ($\cdot10^3$)')

    plt.show()




.. image:: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_periodicity_finder_002.png
    :class: sphx-glr-single-img




There's probably a period of around 10 years (obvious from the
plot), but for this crude a method, there's not enough data to say
much more.


**Total running time of the script:** ( 0 minutes  0.027 seconds)


.. _sphx_glr_download_intro_scipy_auto_examples_solutions_plot_periodicity_finder.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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