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

    Click :ref:`here <sphx_glr_download_auto_examples_plot_2_4_grp_delay_inst_freq_comprison.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_plot_2_4_grp_delay_inst_freq_comprison.py:


=====================================================
Comparison of Instantaneous Frequency and Group Delay
=====================================================

Instantaneous frequency and group delay are very closely related. The former is
the frequency of a signal at a given instant, and the latter is the time delay
of frequency components. As this example shows, they coincide with each other
for a given signal when the time bandwidth product of the signal is
sufficiently high.

Figure 2.5 from the tutorial.



.. image:: /auto_examples/images/sphx_glr_plot_2_4_grp_delay_inst_freq_comprison_001.png
    :class: sphx-glr-single-img





.. code-block:: default


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

    time_instants = np.arange(2, 256)
    sig1 = amgauss(256, 128, 90) * fmlin(256)[0]
    tm, T1 = loctime(sig1)
    fm, B1 = locfreq(sig1)
    ifr1 = inst_freq(sig1, time_instants)[0]
    f1 = np.linspace(0, 0.5 - 1.0 / 256, 256)
    gd1 = group_delay(sig1, f1)

    plt.subplot(211)
    plt.plot(time_instants, ifr1, '*', label='inst_freq')
    plt.plot(gd1, f1, '-', label='group delay')
    plt.xlim(0, 256)
    plt.grid(True)
    plt.legend()
    plt.title("Time-Bandwidth product: {0}".format(T1 * B1))
    plt.xlabel('Time')
    plt.ylabel('Normalized Frequency')


    sig2 = amgauss(256, 128, 30) * fmlin(256, 0.2, 0.4)[0]
    tm, T2 = loctime(sig2)
    fm, B2 = locfreq(sig2)
    ifr2 = inst_freq(sig2, time_instants)[0]
    f2 = np.linspace(0.02, 0.4, 256)
    gd2 = group_delay(sig2, f2)


    plt.subplot(212)
    plt.plot(time_instants, ifr2, '*', label='inst_freq')
    plt.plot(gd2, f2, '-', label='group delay')
    plt.ylim(0.2, 0.4)
    plt.xlim(0, 256)
    plt.grid(True)
    plt.legend()
    plt.title("Time-Bandwidth product: {0}".format(T2 * B2))
    plt.xlabel('Time')
    plt.ylabel('Normalized Frequency')

    plt.subplots_adjust(hspace=0.5)

    plt.show()


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

   **Total running time of the script:** ( 0 minutes  0.420 seconds)


.. _sphx_glr_download_auto_examples_plot_2_4_grp_delay_inst_freq_comprison.py:


.. only :: html

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



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_2_4_grp_delay_inst_freq_comprison.py <plot_2_4_grp_delay_inst_freq_comprison.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_2_4_grp_delay_inst_freq_comprison.ipynb <plot_2_4_grp_delay_inst_freq_comprison.ipynb>`


.. only:: html

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

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