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

    Click :ref:`here <sphx_glr_download_auto_examples_plot_2_2_2_heisenberg_gabor_inequality.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_plot_2_2_2_heisenberg_gabor_inequality.py:


==========================
Heisenbeg-Gabor Inequality
==========================

This example demonstrates the `Heisenberg-Gabor inequality
<https://en.wikipedia.org/wiki/Uncertainty_principle#Signal_processing>`_.

Simply put, the inequality states that the time-bandwidth product of a signal
is lower bound by some constant (in this case normalized to unity). This means
that a signal cannot have arbitrarily high precision in time and frequency
simultaneously.

Figure 2.2 from the tutorial.



.. image:: /auto_examples/images/sphx_glr_plot_2_2_2_heisenberg_gabor_inequality_001.png
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    Time Center: 126.99999999999999
    Time Duration: 31.999999999999996
    Frequency Center: 4.336808689942018e-19
    Frequency Spreading: 0.03125
    Time-bandwidth product: 0.9999999999999999





|


.. code-block:: default


    from tftb.generators import amgauss
    from tftb.processing import loctime, locfreq
    import numpy as np
    import matplotlib.pyplot as plt

    # generate signal
    signal = amgauss(256)
    plt.subplot(211), plt.plot(np.real(signal))
    plt.xlim(0, 256)
    plt.xlabel('Time')
    plt.ylabel('Real part')
    plt.title('Signal')
    plt.grid()
    fsig = np.fft.fftshift(np.abs(np.fft.fft(signal)) ** 2)
    plt.subplot(212), plt.plot(np.linspace(0, 0.5, 256), fsig)
    plt.xlabel('Normalized frequency')
    plt.ylabel('Squared modulus')
    plt.title('Spectrum')
    plt.grid()
    plt.subplots_adjust(hspace=0.5)
    plt.show()

    tm, T = loctime(signal)
    print("Time Center: {}".format(tm))
    print("Time Duration: {}".format(T))
    fm, B = locfreq(signal)
    print("Frequency Center: {}".format(fm))
    print("Frequency Spreading: {}".format(B))
    print("Time-bandwidth product: {}".format(T * B))


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

   **Total running time of the script:** ( 0 minutes  0.372 seconds)


.. _sphx_glr_download_auto_examples_plot_2_2_2_heisenberg_gabor_inequality.py:


.. only :: html

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



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_2_2_2_heisenberg_gabor_inequality.py <plot_2_2_2_heisenberg_gabor_inequality.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_2_2_2_heisenberg_gabor_inequality.ipynb <plot_2_2_2_heisenberg_gabor_inequality.ipynb>`


.. only:: html

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

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