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

    Click :ref:`here <sphx_glr_download_auto_examples_plot_2_7_multicomp_nonstat_stft.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_plot_2_7_multicomp_nonstat_stft.py:


======================================================================
Short time Fourier transform of a multi-component nonstationary signal
======================================================================

Compute and visualize the `STFT <https://en.wikipedia.org/wiki/Short-time_Fourier_transform>`_ of a multi component nonstationary signal.

Figure 2.11 from the tutorial.



.. image:: /auto_examples/images/sphx_glr_plot_2_7_multicomp_nonstat_stft_001.png
    :class: sphx-glr-single-img





.. code-block:: default


    from tftb.generators import fmlin
    from tftb.processing.linear import ShortTimeFourierTransform
    import matplotlib.pyplot as plt
    from scipy.signal import hamming
    import numpy as np
    from mpl_toolkits.axes_grid1 import make_axes_locatable

    N = 128
    x1, _ = fmlin(N, 0, 0.2)
    x2, _ = fmlin(N, 0.3, 0.5)
    x = x1 + x2

    n_fbins = 128
    window = hamming(33)
    tfr, _, _ = ShortTimeFourierTransform(x, timestamps=None, n_fbins=n_fbins,
                                          fwindow=window).run()
    tfr = tfr[:64, :]
    threshold = np.amax(np.abs(tfr)) * 0.05
    tfr[np.abs(tfr) <= threshold] = 0.0 + 1j * 0.0
    tfr = np.abs(tfr) ** 2
    t = np.arange(tfr.shape[1])
    f = np.linspace(0, 0.5, tfr.shape[0])

    T, F = np.meshgrid(t, f)

    fig, axScatter = plt.subplots(figsize=(10, 8))
    axScatter.contour(T, F, tfr, 5)
    axScatter.grid(True)
    axScatter.set_title('Squared modulus of STFT')
    axScatter.set_ylabel('Frequency')
    axScatter.yaxis.set_label_position("right")
    axScatter.set_xlabel('Time')
    divider = make_axes_locatable(axScatter)
    axTime = divider.append_axes("top", 1.2, pad=0.5)
    axFreq = divider.append_axes("left", 1.2, pad=0.5)
    axTime.plot(np.real(x))
    axTime.set_xticklabels([])
    axTime.set_xlim(0, N)
    axTime.set_ylabel('Real part')
    axTime.set_title('Signal in time')
    axTime.grid(True)
    axFreq.plot((abs(np.fft.fftshift(np.fft.fft(x))) ** 2)[::-1][:64], f[:64])
    axFreq.set_yticklabels([])
    axFreq.set_xticklabels([])
    axFreq.invert_xaxis()
    axFreq.set_ylabel('Spectrum')
    axFreq.grid(True)
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  1.083 seconds)


.. _sphx_glr_download_auto_examples_plot_2_7_multicomp_nonstat_stft.py:


.. only :: html

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



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_2_7_multicomp_nonstat_stft.py <plot_2_7_multicomp_nonstat_stft.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_2_7_multicomp_nonstat_stft.ipynb <plot_2_7_multicomp_nonstat_stft.ipynb>`


.. only:: html

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

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