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

    Click :ref:`here <sphx_glr_download_auto_examples_plot_3_4_2_morlet_scalogram_complex_sinusoids.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_plot_3_4_2_morlet_scalogram_complex_sinusoids.py:


===========================================
Morlet Scalogram of a Multicomponent Signal
===========================================

This example demonstrates the visualization of the Morlet scalogram of a signal
containing two complex sinusoids. In a scalogram, the frequency resolution
varies on the scale of the signal. Here, the frequency resolution decreases at
higher frequencies (lower scale).

Figure 3.20 from the tutorial.



.. image:: /auto_examples/images/sphx_glr_plot_3_4_2_morlet_scalogram_complex_sinusoids_001.png
    :class: sphx-glr-single-img





.. code-block:: default


    from tftb.processing import Scalogram
    from tftb.generators import fmconst
    import numpy as np
    from mpl_toolkits.axes_grid1 import make_axes_locatable
    import matplotlib.pyplot as plt

    sig2 = fmconst(128, .15)[0] + fmconst(128, .35)[0]
    tfr, t, freqs, _ = Scalogram(sig2, time_instants=np.arange(1, 129), waveparams=6,
                             fmin=0.05, fmax=0.45, n_voices=128).run()
    tfr = np.abs(tfr) ** 2
    threshold = np.amax(tfr) * 0.05
    tfr[tfr <= threshold] = 0.0
    t, f = np.meshgrid(t, freqs)

    fig, axContour = plt.subplots(figsize=(10, 8))
    axContour.contour(t, f, tfr)
    axContour.grid(True)
    axContour.set_title("Morlet scalogram")
    axContour.set_ylabel('Frequency')
    axContour.yaxis.set_label_position('right')
    axContour.set_xlabel('Time')

    divider = make_axes_locatable(axContour)
    axTime = divider.append_axes("top", 1.2, pad=0.5)
    axFreq = divider.append_axes("left", 1.2, pad=0.5)
    axTime.plot(np.real(sig2))
    axTime.set_xticklabels([])
    axTime.set_xlim(0, 128)
    axTime.set_ylabel('Real part')
    axTime.set_title('Signal in time')
    axTime.grid(True)
    freq_y = np.linspace(0, 0.5, sig2.shape[0] / 2)
    freq_x = (abs(np.fft.fftshift(np.fft.fft(sig2))) ** 2)[::-1][:64]
    axFreq.plot(freq_x, freq_y)
    axFreq.set_ylim(0.05, 0.45)
    axFreq.set_yticklabels([])
    axFreq.set_xticklabels([])
    axFreq.grid(True)
    axFreq.set_ylabel('Spectrum')
    axFreq.invert_xaxis()
    axFreq.grid(True)
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  1.043 seconds)


.. _sphx_glr_download_auto_examples_plot_3_4_2_morlet_scalogram_complex_sinusoids.py:


.. only :: html

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



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_3_4_2_morlet_scalogram_complex_sinusoids.py <plot_3_4_2_morlet_scalogram_complex_sinusoids.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_3_4_2_morlet_scalogram_complex_sinusoids.ipynb <plot_3_4_2_morlet_scalogram_complex_sinusoids.ipynb>`


.. only:: html

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

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