:orphan:



.. _sphx_glr_auto_examples:

.. _general_examples:

General examples
----------------

General-purpose and introductory examples for PyTFTB



.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the Wigner-Ville distribution of a Dirac impulse function, and shows ...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_2_3_impulse_wv_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_2_3_impulse_wv.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_2_3_impulse_wv

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the Bertrand distribution of a signal with hyperbolic group delay. The distr...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_2_2_bertrand_hyperbolic_gd_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_2_2_bertrand_hyperbolic_gd.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_2_2_bertrand_hyperbolic_gd

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the wireframe plot of the Wigner-Ville distribution of a chirp. The WV distr...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_1_1_wv_wireframe_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_1_1_wv_wireframe.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_1_1_wv_wireframe

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The active Unterberger distribution is the only localized bi-frequency kernel distribution whic...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_2_2_unterberger_hyperbolic_gd_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_2_2_unterberger_hyperbolic_gd.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_2_2_unterberger_hyperbolic_gd

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the D-Flandrin distribution of a signal having hyperbolic group delay. This ...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_2_2_dflandrin_hyperbolic_gd_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_2_2_dflandrin_hyperbolic_gd.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_2_2_dflandrin_hyperbolic_gd

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the Wigner Ville distribution of a signal composed from a Gaussian at...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_1_2_sin_gauss_wv_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_1_2_sin_gauss_wv.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_1_2_sin_gauss_wv

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the Wigner-Ville distribution of a noisy chirp signal. The linear frequency ...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_5_4_2_wv_noisy_chirp_thumb.png

        :ref:`sphx_glr_auto_examples_plot_5_4_2_wv_noisy_chirp.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_5_4_2_wv_noisy_chirp

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The signal to be analyzed contains two linear frequency modulations, each with a different slop...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_5_4_2_wv_simultaneous_chirp_thumb.png

        :ref:`sphx_glr_auto_examples_plot_5_4_2_wv_simultaneous_chirp.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_5_4_2_wv_simultaneous_chirp

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the Wigner-Ville distribution of a Doppler signal. The signal steadily rises...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_1_1_doppler_wigner_ville_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_1_1_doppler_wigner_ville.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_1_1_doppler_wigner_ville

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the WVD of and analytic Gaussian atom. As seen in Figure 4.6, the WVD of a r...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_1_1_wv_analytic_signal_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_1_1_wv_analytic_signal.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_1_1_wv_analytic_signal

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the Wigner-Ville distribution of a real valued Gaussian atom. If a signal is...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_1_1_wv_real_signal_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_1_1_wv_real_signal.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_1_1_wv_real_signal

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Generate a Doppler Signal.">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_2_6_monocomp_nonstat_doppler_thumb.png

        :ref:`sphx_glr_auto_examples_plot_2_6_monocomp_nonstat_doppler.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_2_6_monocomp_nonstat_doppler

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Generate a mono-component nonstationary signal with linear frequency modulation and Gaussian am...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_2_6_monocomp_nonstat_linfreq_gaussamp_thumb.png

        :ref:`sphx_glr_auto_examples_plot_2_6_monocomp_nonstat_linfreq_gaussamp.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_2_6_monocomp_nonstat_linfreq_gaussamp

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the pseudo Wigner Ville distribution of a signal composed from a Gaus...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_1_2_sin_gauss_pwv_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_1_2_sin_gauss_pwv.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_1_2_sin_gauss_pwv

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Construct a chirp signal and visualize its `Wigner-Ville distribution &lt;https://en.wikipedia.org...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_1_3_1_chirp_wv_thumb.png

        :ref:`sphx_glr_auto_examples_plot_1_3_1_chirp_wv.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_1_3_1_chirp_wv

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Construct a chirp and estimate its `instantaneous frequency &lt;https://en.wikipedia.org/wiki/Inst...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_2_3_instantaneous_frequency_thumb.png

        :ref:`sphx_glr_auto_examples_plot_2_3_instantaneous_frequency.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_2_3_instantaneous_frequency

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the effect of an analysis window which is long in time on the time-frequency...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_1_4_frequency_resolution_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_1_4_frequency_resolution.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_1_4_frequency_resolution

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how PyTFTB is used to generate a signal with linear frequency modulation. Su...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_1_3_1_chirp_thumb.png

        :ref:`sphx_glr_auto_examples_plot_1_3_1_chirp.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_1_3_1_chirp

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the Margenau-Hill distribution of a signal composed of two chirps wit...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_1_4_margenau_hill_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_1_4_margenau_hill.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_1_4_margenau_hill

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the WV distribution of four Gaussian atoms, each localized at the corner of ...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_1_1_wv_atoms_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_1_1_wv_atoms.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_1_1_wv_atoms

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates that only the shortest possible window can provide ideal resolution i...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_1_4_time_resolution_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_1_4_time_resolution.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_1_4_time_resolution

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example visualizes a spectrogram of two chirp signals which are well separated in frequenc...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_4_1_distant_components_long_gaussian_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_4_1_distant_components_long_gaussian.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_4_1_distant_components_long_gaussian

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example visualizes the spectrogram of two &quot;parallel&quot; chirps, using a Gaussian window funct...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_4_1_chirps_spectrogram_short_gaussian_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_4_1_chirps_spectrogram_short_gaussian.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_4_1_chirps_spectrogram_short_gaussian

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example visualizes the spectrogram of two &quot;parallel&quot; chirps, using a Gaussian window funct...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_4_1_chirps_spectrogram_long_gaussian_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_4_1_chirps_spectrogram_long_gaussian.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_4_1_chirps_spectrogram_long_gaussian

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Figure 3.17 from the tutorial.">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_4_1_distant_components_short_gaussian_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_4_1_distant_components_short_gaussian.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_4_1_distant_components_short_gaussian

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the Wigner-Ville distribution of a signal composed of two chirps with...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_1_3_chirps_wvd_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_1_3_chirps_wvd.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_1_3_chirps_wvd

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="For wideband signals, the narrow band ambiguity function is not appropriate for wideband signal...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_2_3_wideband_ambiguity_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_2_3_wideband_ambiguity.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_2_3_wideband_ambiguity

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Generate a monocomponent nonstationary signal with constant frequency modulation and one-sided ...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_2_6_monocomp_nonstat_constfreq_expamp_thumb.png

        :ref:`sphx_glr_auto_examples_plot_2_6_monocomp_nonstat_constfreq_expamp.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_2_6_monocomp_nonstat_constfreq_expamp

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Constuct a chirp and estimates its `group delay &lt;https://en.wikipedia.org/wiki/Group_delay_and_...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_2_4_group_delay_thumb.png

        :ref:`sphx_glr_auto_examples_plot_2_4_group_delay.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_2_4_group_delay

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the Pseudo Wigner-Ville distribution of four Gaussian atoms located at the c...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_1_1_pwv_atoms_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_1_1_pwv_atoms.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_1_1_pwv_atoms

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Generate a noisy chirp and visualize its Wigner-Ville spectrum.">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_1_3_1_noisy_chirp_wv_thumb.png

        :ref:`sphx_glr_auto_examples_plot_1_3_1_noisy_chirp_wv.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_1_3_1_noisy_chirp_wv

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how to generate a chirp signal, with some analytical gaussian noise, and the...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_1_3_1_noisy_chirp_thumb.png

        :ref:`sphx_glr_auto_examples_plot_1_3_1_noisy_chirp.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_1_3_1_noisy_chirp

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Figure 3.10 from the tutorial.">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_3_2_biorthonormal_window_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_3_2_biorthonormal_window.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_3_2_biorthonormal_window

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the construction of a signal containing two transient components, hav...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_1_4_atoms_hamming_stft_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_1_4_atoms_hamming_stft.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_1_4_atoms_hamming_stft

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the construction of a monocomponent signal with linear frequency modu...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_2_6_monocomp_nonstat_colored_gaussian_noise_thumb.png

        :ref:`sphx_glr_auto_examples_plot_2_6_monocomp_nonstat_colored_gaussian_noise.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_2_6_monocomp_nonstat_colored_gaussian_noise

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the effect of an analysis window which is short in time on the time-frequenc...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_1_4_atoms_short_hamming_stft_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_1_4_atoms_short_hamming_stft.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_1_4_atoms_short_hamming_stft

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Construct a chirp and plot its `energy spectral density &lt;https://en.wikipedia.org/wiki/Spectral...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_1_3_1_chirp_spectrum_thumb.png

        :ref:`sphx_glr_auto_examples_plot_1_3_1_chirp_spectrum.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_1_3_1_chirp_spectrum

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the narrow band ambiguity function (AF) of a signal composed of two c...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_1_3_chirps_ambifunb_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_1_3_chirps_ambifunb.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_1_3_chirps_ambifunb

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Figure 3.4 from the tutorial.">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_1_2_stft_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_1_2_stft.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_1_2_stft

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the simple use of a Spectrogram to localize a signal in time and freq...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_1_3_3_transient_spectrogram_thumb.png

        :ref:`sphx_glr_auto_examples_plot_1_3_3_transient_spectrogram.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_1_3_3_transient_spectrogram

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example plots the scalogram of a Dirac impulse functions. This shows the behaviour of the ...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_4_2_morlet_scalogram_dirac_impulse_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_4_2_morlet_scalogram_dirac_impulse.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_4_2_morlet_scalogram_dirac_impulse

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Figure 3.11 from the tutorial.">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_3_2_biorthonormal_window_gabor_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_3_2_biorthonormal_window_gabor.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_3_2_biorthonormal_window_gabor

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Generate a noisy chirp and plot its energy spectrum.">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_1_3_1_noisy_chirp_spectrum_thumb.png

        :ref:`sphx_glr_auto_examples_plot_1_3_1_noisy_chirp_spectrum.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_1_3_1_noisy_chirp_spectrum

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the use of the Hough transform to extract the estimates of a chirp si...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_5_4_2_hough_noisy_chirp_thumb.png

        :ref:`sphx_glr_auto_examples_plot_5_4_2_hough_noisy_chirp.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_5_4_2_hough_noisy_chirp

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Compute the Hough transform of the Wigner-Ville distribution of a signal composed of two chirps...">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_5_4_2_hough_simultaneous_chirp_thumb.png

        :ref:`sphx_glr_auto_examples_plot_5_4_2_hough_simultaneous_chirp.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_5_4_2_hough_simultaneous_chirp

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Figure 3.13 from the tutorial.">

.. only:: html

    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_3_2_biorthonormal_window_oversampled_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_3_2_biorthonormal_window_oversampled.py`

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_3_3_2_biorthonormal_window_oversampled

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Figure 3.3 from the tutorial.">

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    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_1_2_spectrum_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_1_2_spectrum.py`

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    </div>


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   /auto_examples/plot_3_1_2_spectrum

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    <div class="sphx-glr-thumbcontainer" tooltip="This example uses Friedman&#x27;s method to calculate the instantaneous frequency density of a hybri...">

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    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_3_6_friedman_instfreq_density_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_3_6_friedman_instfreq_density.py`

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   /auto_examples/plot_4_3_6_friedman_instfreq_density

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    <div class="sphx-glr-thumbcontainer" tooltip="Generate a signal that has localized characteristics in both time and frequency and compute the...">

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    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_2_2_1_time_freq_localization_thumb.png

        :ref:`sphx_glr_auto_examples_plot_2_2_1_time_freq_localization.py`

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.. toctree::
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   /auto_examples/plot_2_2_1_time_freq_localization

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    <div class="sphx-glr-thumbcontainer" tooltip="Figure 2.10 from the tutorial.">

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    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_2_7_multicomp_nonstat_instfreq_grpdlay_thumb.png

        :ref:`sphx_glr_auto_examples_plot_2_7_multicomp_nonstat_instfreq_grpdlay.py`

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.. toctree::
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   /auto_examples/plot_2_7_multicomp_nonstat_instfreq_grpdlay

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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the `Heisenberg-Gabor inequality &lt;https://en.wikipedia.org/wiki/Uncer...">

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    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_2_2_2_heisenberg_gabor_inequality_thumb.png

        :ref:`sphx_glr_auto_examples_plot_2_2_2_heisenberg_gabor_inequality.py`

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   /auto_examples/plot_2_2_2_heisenberg_gabor_inequality

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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how to generate a noisy transient signal with the following characteristics:">

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    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_1_3_3_transient_thumb.png

        :ref:`sphx_glr_auto_examples_plot_1_3_3_transient.py`

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   /auto_examples/plot_1_3_3_transient

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    <div class="sphx-glr-thumbcontainer" tooltip="This example compares the spectrogram and the reassigned spectrogram of a hybrid signal (contai...">

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    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_3_2_reassigned_spectrogram_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_3_2_reassigned_spectrogram.py`

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.. toctree::
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   /auto_examples/plot_4_3_2_reassigned_spectrogram

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    <div class="sphx-glr-thumbcontainer" tooltip="Instantaneous frequency and group delay are very closely related. The former is the frequency o...">

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    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_2_4_grp_delay_inst_freq_comprison_thumb.png

        :ref:`sphx_glr_auto_examples_plot_2_4_grp_delay_inst_freq_comprison.py`

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.. toctree::
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   /auto_examples/plot_2_4_grp_delay_inst_freq_comprison

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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the effect of frequency-dependent smoothing that is accomplished in a...">

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    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_4_2_2_morlet_scalogram_atoms_thumb.png

        :ref:`sphx_glr_auto_examples_plot_4_2_2_morlet_scalogram_atoms.py`

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.. toctree::
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   /auto_examples/plot_4_2_2_morlet_scalogram_atoms

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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the visualization of the Morlet scalogram of a signal containing two ...">

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    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_3_4_2_morlet_scalogram_complex_sinusoids_thumb.png

        :ref:`sphx_glr_auto_examples_plot_3_4_2_morlet_scalogram_complex_sinusoids.py`

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    </div>


.. toctree::
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   /auto_examples/plot_3_4_2_morlet_scalogram_complex_sinusoids

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    <div class="sphx-glr-thumbcontainer" tooltip="Compute and visualize the `STFT &lt;https://en.wikipedia.org/wiki/Short-time_Fourier_transform&gt;`_ ...">

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    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_2_7_multicomp_nonstat_stft_thumb.png

        :ref:`sphx_glr_auto_examples_plot_2_7_multicomp_nonstat_stft.py`

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   /auto_examples/plot_2_7_multicomp_nonstat_stft
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