:orphan:

.. _general_examples:

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

General-purpose and introductory examples for PyTFTB



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    <div class="sphx-glr-thumbnails">


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_2_3_impulse_wv_thumb.png
    :alt: Wigner-Ville Distribution of a Dirac Impulse Function

  :ref:`sphx_glr_auto_examples_plot_4_2_3_impulse_wv.py`

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      <div class="sphx-glr-thumbnail-title">Wigner-Ville Distribution of a Dirac Impulse Function</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_2_2_bertrand_hyperbolic_gd_thumb.png
    :alt: Bertrand Distribution of a Hyperbolic Group Delay Signal

  :ref:`sphx_glr_auto_examples_plot_4_2_2_bertrand_hyperbolic_gd.py`

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      <div class="sphx-glr-thumbnail-title">Bertrand Distribution of a Hyperbolic Group Delay Signal</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_1_1_wv_wireframe_thumb.png
    :alt: Wigner-Ville distribution of a Chirp

  :ref:`sphx_glr_auto_examples_plot_4_1_1_wv_wireframe.py`

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      <div class="sphx-glr-thumbnail-title">Wigner-Ville distribution of a Chirp</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_2_2_unterberger_hyperbolic_gd_thumb.png
    :alt: Unterberger distribution of a hyperbolic group delay signal

  :ref:`sphx_glr_auto_examples_plot_4_2_2_unterberger_hyperbolic_gd.py`

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      <div class="sphx-glr-thumbnail-title">Unterberger distribution of a hyperbolic group delay signal</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_2_2_dflandrin_hyperbolic_gd_thumb.png
    :alt: D-Flandrin Distribution of a Hyperbolic Group Delay Signal

  :ref:`sphx_glr_auto_examples_plot_4_2_2_dflandrin_hyperbolic_gd.py`

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      <div class="sphx-glr-thumbnail-title">D-Flandrin Distribution of a Hyperbolic Group Delay Signal</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_1_2_sin_gauss_wv_thumb.png
    :alt: Wigner Ville distribution of a Gaussian Atom and a Complex Sinusoid

  :ref:`sphx_glr_auto_examples_plot_4_1_2_sin_gauss_wv.py`

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      <div class="sphx-glr-thumbnail-title">Wigner Ville distribution of a Gaussian Atom and a Complex Sinusoid</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_5_4_2_wv_noisy_chirp_thumb.png
    :alt: Wigner-Ville Distribution of a Noisy Chirp

  :ref:`sphx_glr_auto_examples_plot_5_4_2_wv_noisy_chirp.py`

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      <div class="sphx-glr-thumbnail-title">Wigner-Ville Distribution of a Noisy Chirp</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_5_4_2_wv_simultaneous_chirp_thumb.png
    :alt: Wigner Ville Distribution of Two Simultaneous Chirps

  :ref:`sphx_glr_auto_examples_plot_5_4_2_wv_simultaneous_chirp.py`

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      <div class="sphx-glr-thumbnail-title">Wigner Ville Distribution of Two Simultaneous Chirps</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_1_1_doppler_wigner_ville_thumb.png
    :alt: Wigner-Ville Distribution of a Doppler Signal

  :ref:`sphx_glr_auto_examples_plot_4_1_1_doppler_wigner_ville.py`

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      <div class="sphx-glr-thumbnail-title">Wigner-Ville Distribution of a Doppler Signal</div>
    </div>


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    <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...">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_1_1_wv_analytic_signal_thumb.png
    :alt: Wigner Ville Distribution of Analytic Gaussian Atoms

  :ref:`sphx_glr_auto_examples_plot_4_1_1_wv_analytic_signal.py`

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      <div class="sphx-glr-thumbnail-title">Wigner Ville Distribution of Analytic Gaussian Atoms</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_1_1_wv_real_signal_thumb.png
    :alt: Sampling Effects on the Wigner-Ville Distribution of a Real Valued Gaussian Atom

  :ref:`sphx_glr_auto_examples_plot_4_1_1_wv_real_signal.py`

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      <div class="sphx-glr-thumbnail-title">Sampling Effects on the Wigner-Ville Distribution of a Real Valued Gaussian Atom</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_2_6_monocomp_nonstat_doppler_thumb.png
    :alt: Doppler Signal

  :ref:`sphx_glr_auto_examples_plot_2_6_monocomp_nonstat_doppler.py`

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      <div class="sphx-glr-thumbnail-title">Doppler Signal</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_2_6_monocomp_nonstat_linfreq_gaussamp_thumb.png
    :alt: Linear Frequency and Gaussian Amplitude Modulation

  :ref:`sphx_glr_auto_examples_plot_2_6_monocomp_nonstat_linfreq_gaussamp.py`

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      <div class="sphx-glr-thumbnail-title">Linear Frequency and Gaussian Amplitude Modulation</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_1_2_sin_gauss_pwv_thumb.png
    :alt: Pseudo-Wigner-Ville Distribution of a Gaussian Atom and a Complex Sinusoid

  :ref:`sphx_glr_auto_examples_plot_4_1_2_sin_gauss_pwv.py`

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      <div class="sphx-glr-thumbnail-title">Pseudo-Wigner-Ville Distribution of a Gaussian Atom and a Complex Sinusoid</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_1_3_1_chirp_wv_thumb.png
    :alt: Wigner-Ville Distribution of a Chirp

  :ref:`sphx_glr_auto_examples_plot_1_3_1_chirp_wv.py`

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      <div class="sphx-glr-thumbnail-title">Wigner-Ville Distribution of a Chirp</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_2_3_instantaneous_frequency_thumb.png
    :alt: Estimate the Instantaneous Freuqncy of a Chirp

  :ref:`sphx_glr_auto_examples_plot_2_3_instantaneous_frequency.py`

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      <div class="sphx-glr-thumbnail-title">Estimate the Instantaneous Freuqncy of a Chirp</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_1_4_frequency_resolution_thumb.png
    :alt: Time-frequency Resolution: Long Analysis Window

  :ref:`sphx_glr_auto_examples_plot_3_1_4_frequency_resolution.py`

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      <div class="sphx-glr-thumbnail-title">Time-frequency Resolution: Long Analysis Window</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_1_3_1_chirp_thumb.png
    :alt: Linear Frequency Modulation

  :ref:`sphx_glr_auto_examples_plot_1_3_1_chirp.py`

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      <div class="sphx-glr-thumbnail-title">Linear Frequency Modulation</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_1_1_wv_atoms_thumb.png
    :alt: Wigner-Ville Distribution of Gaussian Atoms

  :ref:`sphx_glr_auto_examples_plot_4_1_1_wv_atoms.py`

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      <div class="sphx-glr-thumbnail-title">Wigner-Ville Distribution of Gaussian Atoms</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_1_4_time_resolution_thumb.png
    :alt: Ideal time resolution

  :ref:`sphx_glr_auto_examples_plot_3_1_4_time_resolution.py`

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      <div class="sphx-glr-thumbnail-title">Ideal time resolution</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_4_1_chirps_spectrogram_short_gaussian_thumb.png
    :alt: Spectrogram of Parallel Chirps with Short Gaussian Analysis Window

  :ref:`sphx_glr_auto_examples_plot_3_4_1_chirps_spectrogram_short_gaussian.py`

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      <div class="sphx-glr-thumbnail-title">Spectrogram of Parallel Chirps with Short Gaussian Analysis Window</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_1_4_margenau_hill_thumb.png
    :alt: Margenau-Hill Representation of Chirps with Different Slopes

  :ref:`sphx_glr_auto_examples_plot_4_1_4_margenau_hill.py`

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      <div class="sphx-glr-thumbnail-title">Margenau-Hill Representation of Chirps with Different Slopes</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_4_1_distant_components_short_gaussian_thumb.png
    :alt: Distant Chirps with a Short Gaussian Analysis Window

  :ref:`sphx_glr_auto_examples_plot_3_4_1_distant_components_short_gaussian.py`

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      <div class="sphx-glr-thumbnail-title">Distant Chirps with a Short Gaussian Analysis Window</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_4_1_distant_components_long_gaussian_thumb.png
    :alt: Distant Chirps with a Long Gaussian Analysis Window

  :ref:`sphx_glr_auto_examples_plot_3_4_1_distant_components_long_gaussian.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Distant Chirps with a Long Gaussian Analysis Window</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_4_1_chirps_spectrogram_long_gaussian_thumb.png
    :alt: Spectrogram of Parallel Chirps with a Long Gaussian Analysis Window

  :ref:`sphx_glr_auto_examples_plot_3_4_1_chirps_spectrogram_long_gaussian.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Spectrogram of Parallel Chirps with a Long Gaussian Analysis Window</div>
    </div>


.. 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

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_1_3_chirps_wvd_thumb.png
    :alt: Wigner-Ville Distribution of Chirps with Different Slopes

  :ref:`sphx_glr_auto_examples_plot_4_1_3_chirps_wvd.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Wigner-Ville Distribution of Chirps with Different Slopes</div>
    </div>


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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_2_3_wideband_ambiguity_thumb.png
    :alt: Wideband Ambiguity Function of an Altes Signal

  :ref:`sphx_glr_auto_examples_plot_4_2_3_wideband_ambiguity.py`

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      <div class="sphx-glr-thumbnail-title">Wideband Ambiguity Function of an Altes Signal</div>
    </div>


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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_2_6_monocomp_nonstat_constfreq_expamp_thumb.png
    :alt: Monocomponent Nonstationary Signal with Constant Frequency Modulation and One-Sided Exponential Amplitude Modulation

  :ref:`sphx_glr_auto_examples_plot_2_6_monocomp_nonstat_constfreq_expamp.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Monocomponent Nonstationary Signal with Constant Frequency Modulation and One-Sided Exponential Amplitude Modulation</div>
    </div>


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    <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

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_2_4_group_delay_thumb.png
    :alt: Group Delay Estimation of a Chirp

  :ref:`sphx_glr_auto_examples_plot_2_4_group_delay.py`

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      <div class="sphx-glr-thumbnail-title">Group Delay Estimation of a Chirp</div>
    </div>


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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_1_1_pwv_atoms_thumb.png
    :alt: Pseudo Wigner-Ville Distribution of Gaussian Atoms

  :ref:`sphx_glr_auto_examples_plot_4_1_1_pwv_atoms.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Pseudo Wigner-Ville Distribution of Gaussian Atoms</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_1_3_1_noisy_chirp_wv_thumb.png
    :alt: Wigner-Ville Distribution of a Noisy Chirp

  :ref:`sphx_glr_auto_examples_plot_1_3_1_noisy_chirp_wv.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Wigner-Ville Distribution of a Noisy Chirp</div>
    </div>


.. 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

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_1_3_1_noisy_chirp_thumb.png
    :alt: Generating a Noisy Chirp

  :ref:`sphx_glr_auto_examples_plot_1_3_1_noisy_chirp.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Generating a Noisy Chirp</div>
    </div>


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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_3_2_biorthonormal_window_thumb.png
    :alt: Biorthonormal Window Function

  :ref:`sphx_glr_auto_examples_plot_3_3_2_biorthonormal_window.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Biorthonormal Window Function</div>
    </div>


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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_2_6_monocomp_nonstat_colored_gaussian_noise_thumb.png
    :alt: Noisy Monocomponent Chirp

  :ref:`sphx_glr_auto_examples_plot_2_6_monocomp_nonstat_colored_gaussian_noise.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Noisy Monocomponent Chirp</div>
    </div>


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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_1_4_atoms_hamming_stft_thumb.png
    :alt: STFT of Gaussian Wave Packets with a Hamming Analysis Window

  :ref:`sphx_glr_auto_examples_plot_3_1_4_atoms_hamming_stft.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">STFT of Gaussian Wave Packets with a Hamming Analysis Window</div>
    </div>


.. 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

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_1_4_atoms_short_hamming_stft_thumb.png
    :alt: Time-frequency Resolution: Short Analysis Window

  :ref:`sphx_glr_auto_examples_plot_3_1_4_atoms_short_hamming_stft.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Time-frequency Resolution: Short Analysis Window</div>
    </div>


.. 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

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_1_3_1_chirp_spectrum_thumb.png
    :alt: Energy Spectral Density of a Chirp

  :ref:`sphx_glr_auto_examples_plot_1_3_1_chirp_spectrum.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Energy Spectral Density of a Chirp</div>
    </div>


.. 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

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_1_3_chirps_ambifunb_thumb.png
    :alt: Narrow Band Ambiguity Function of Chirps with Different Slopes

  :ref:`sphx_glr_auto_examples_plot_4_1_3_chirps_ambifunb.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Narrow Band Ambiguity Function of Chirps with Different Slopes</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_1_2_stft_thumb.png
    :alt: STFT of an Audio Signal

  :ref:`sphx_glr_auto_examples_plot_3_1_2_stft.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">STFT of an Audio Signal</div>
    </div>


.. 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

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_1_3_3_transient_spectrogram_thumb.png
    :alt: Spectrogram of a Noisy Transient Signal

  :ref:`sphx_glr_auto_examples_plot_1_3_3_transient_spectrogram.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Spectrogram of a Noisy Transient Signal</div>
    </div>


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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_4_2_morlet_scalogram_dirac_impulse_thumb.png
    :alt: Morlet Scalogram of a Dirac Impulse

  :ref:`sphx_glr_auto_examples_plot_3_4_2_morlet_scalogram_dirac_impulse.py`

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      <div class="sphx-glr-thumbnail-title">Morlet Scalogram of a Dirac Impulse</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_3_2_biorthonormal_window_gabor_thumb.png
    :alt: Gabor Representation of a Chirp

  :ref:`sphx_glr_auto_examples_plot_3_3_2_biorthonormal_window_gabor.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gabor Representation of a Chirp</div>
    </div>


.. raw:: html

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

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_1_3_1_noisy_chirp_spectrum_thumb.png
    :alt: Energy Spectrum of a Noisy Chirp

  :ref:`sphx_glr_auto_examples_plot_1_3_1_noisy_chirp_spectrum.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Energy Spectrum of a Noisy Chirp</div>
    </div>


.. 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

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_5_4_2_hough_noisy_chirp_thumb.png
    :alt: Wigner-Hough Transform of a Chirp

  :ref:`sphx_glr_auto_examples_plot_5_4_2_hough_noisy_chirp.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Wigner-Hough Transform of a Chirp</div>
    </div>


.. 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

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_5_4_2_hough_simultaneous_chirp_thumb.png
    :alt: Hough-Wigner Transform of Two Simultaneous Chirps

  :ref:`sphx_glr_auto_examples_plot_5_4_2_hough_simultaneous_chirp.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Hough-Wigner Transform of Two Simultaneous Chirps</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_3_2_biorthonormal_window_oversampled_thumb.png
    :alt: Gabor Representation of a Chirp with Oversampling

  :ref:`sphx_glr_auto_examples_plot_3_3_2_biorthonormal_window_oversampled.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gabor Representation of a Chirp with Oversampling</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_1_2_spectrum_thumb.png
    :alt: Energy Spectrum of an Audio Signal

  :ref:`sphx_glr_auto_examples_plot_3_1_2_spectrum.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Energy Spectrum of an Audio Signal</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_3_6_friedman_instfreq_density_thumb.png
    :alt: Friedman's Instantaneous Frequency Density Calculation

  :ref:`sphx_glr_auto_examples_plot_4_3_6_friedman_instfreq_density.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Friedman's Instantaneous Frequency Density Calculation</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_2_2_1_time_freq_localization_thumb.png
    :alt: Time and Frequency Localization Characteristics

  :ref:`sphx_glr_auto_examples_plot_2_2_1_time_freq_localization.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Time and Frequency Localization Characteristics</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_2_7_multicomp_nonstat_instfreq_grpdlay_thumb.png
    :alt: Instantatneous Frequency and Group Delay Estimation of a Multi-Component Nonstationary Signal

  :ref:`sphx_glr_auto_examples_plot_2_7_multicomp_nonstat_instfreq_grpdlay.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Instantatneous Frequency and Group Delay Estimation of a Multi-Component Nonstationary Signal</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_2_2_2_heisenberg_gabor_inequality_thumb.png
    :alt: Heisenbeg-Gabor Inequality

  :ref:`sphx_glr_auto_examples_plot_2_2_2_heisenberg_gabor_inequality.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Heisenbeg-Gabor Inequality</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_1_3_3_transient_thumb.png
    :alt: Spectrum of a Noisy Transient Signal

  :ref:`sphx_glr_auto_examples_plot_1_3_3_transient.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Spectrum of a Noisy Transient Signal</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_3_2_reassigned_spectrogram_thumb.png
    :alt: Comparison of a Spectrogram and a Reassigned Spectrogram

  :ref:`sphx_glr_auto_examples_plot_4_3_2_reassigned_spectrogram.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Comparison of a Spectrogram and a Reassigned Spectrogram</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_2_4_grp_delay_inst_freq_comprison_thumb.png
    :alt: Comparison of Instantaneous Frequency and Group Delay

  :ref:`sphx_glr_auto_examples_plot_2_4_grp_delay_inst_freq_comprison.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Comparison of Instantaneous Frequency and Group Delay</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_4_2_2_morlet_scalogram_atoms_thumb.png
    :alt: Morlet Scalogram of Gaussian Atoms

  :ref:`sphx_glr_auto_examples_plot_4_2_2_morlet_scalogram_atoms.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Morlet Scalogram of Gaussian Atoms</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_3_4_2_morlet_scalogram_complex_sinusoids_thumb.png
    :alt: Morlet Scalogram of a Multicomponent Signal

  :ref:`sphx_glr_auto_examples_plot_3_4_2_morlet_scalogram_complex_sinusoids.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Morlet Scalogram of a Multicomponent Signal</div>
    </div>


.. raw:: html

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

.. only:: html

  .. image:: /auto_examples/images/thumb/sphx_glr_plot_2_7_multicomp_nonstat_stft_thumb.png
    :alt: Short time Fourier transform of a multi-component nonstationary signal

  :ref:`sphx_glr_auto_examples_plot_2_7_multicomp_nonstat_stft.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Short time Fourier transform of a multi-component nonstationary signal</div>
    </div>


.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_4_2_3_impulse_wv
   /auto_examples/plot_4_2_2_bertrand_hyperbolic_gd
   /auto_examples/plot_4_1_1_wv_wireframe
   /auto_examples/plot_4_2_2_unterberger_hyperbolic_gd
   /auto_examples/plot_4_2_2_dflandrin_hyperbolic_gd
   /auto_examples/plot_4_1_2_sin_gauss_wv
   /auto_examples/plot_5_4_2_wv_noisy_chirp
   /auto_examples/plot_5_4_2_wv_simultaneous_chirp
   /auto_examples/plot_4_1_1_doppler_wigner_ville
   /auto_examples/plot_4_1_1_wv_analytic_signal
   /auto_examples/plot_4_1_1_wv_real_signal
   /auto_examples/plot_2_6_monocomp_nonstat_doppler
   /auto_examples/plot_2_6_monocomp_nonstat_linfreq_gaussamp
   /auto_examples/plot_4_1_2_sin_gauss_pwv
   /auto_examples/plot_1_3_1_chirp_wv
   /auto_examples/plot_2_3_instantaneous_frequency
   /auto_examples/plot_3_1_4_frequency_resolution
   /auto_examples/plot_1_3_1_chirp
   /auto_examples/plot_4_1_1_wv_atoms
   /auto_examples/plot_3_1_4_time_resolution
   /auto_examples/plot_3_4_1_chirps_spectrogram_short_gaussian
   /auto_examples/plot_4_1_4_margenau_hill
   /auto_examples/plot_3_4_1_distant_components_short_gaussian
   /auto_examples/plot_3_4_1_distant_components_long_gaussian
   /auto_examples/plot_3_4_1_chirps_spectrogram_long_gaussian
   /auto_examples/plot_4_1_3_chirps_wvd
   /auto_examples/plot_4_2_3_wideband_ambiguity
   /auto_examples/plot_2_6_monocomp_nonstat_constfreq_expamp
   /auto_examples/plot_2_4_group_delay
   /auto_examples/plot_4_1_1_pwv_atoms
   /auto_examples/plot_1_3_1_noisy_chirp_wv
   /auto_examples/plot_1_3_1_noisy_chirp
   /auto_examples/plot_3_3_2_biorthonormal_window
   /auto_examples/plot_2_6_monocomp_nonstat_colored_gaussian_noise
   /auto_examples/plot_3_1_4_atoms_hamming_stft
   /auto_examples/plot_3_1_4_atoms_short_hamming_stft
   /auto_examples/plot_1_3_1_chirp_spectrum
   /auto_examples/plot_4_1_3_chirps_ambifunb
   /auto_examples/plot_3_1_2_stft
   /auto_examples/plot_1_3_3_transient_spectrogram
   /auto_examples/plot_3_4_2_morlet_scalogram_dirac_impulse
   /auto_examples/plot_3_3_2_biorthonormal_window_gabor
   /auto_examples/plot_1_3_1_noisy_chirp_spectrum
   /auto_examples/plot_5_4_2_hough_noisy_chirp
   /auto_examples/plot_5_4_2_hough_simultaneous_chirp
   /auto_examples/plot_3_3_2_biorthonormal_window_oversampled
   /auto_examples/plot_3_1_2_spectrum
   /auto_examples/plot_4_3_6_friedman_instfreq_density
   /auto_examples/plot_2_2_1_time_freq_localization
   /auto_examples/plot_2_7_multicomp_nonstat_instfreq_grpdlay
   /auto_examples/plot_2_2_2_heisenberg_gabor_inequality
   /auto_examples/plot_1_3_3_transient
   /auto_examples/plot_4_3_2_reassigned_spectrogram
   /auto_examples/plot_2_4_grp_delay_inst_freq_comprison
   /auto_examples/plot_4_2_2_morlet_scalogram_atoms
   /auto_examples/plot_3_4_2_morlet_scalogram_complex_sinusoids
   /auto_examples/plot_2_7_multicomp_nonstat_stft


.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-gallery

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download all examples in Python source code: auto_examples_python.zip </auto_examples/auto_examples_python.zip>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </auto_examples/auto_examples_jupyter.zip>`


.. only:: html

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

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