.. _sphx_glr_api_gallery_signal_processing_wavelets:

Wavelets
--------

Bases that are local in both time and scale.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="In his 1909 dissertation, published in 1910, Alfréd Haar built an orthonormal basis from a single step function: the difference between the two halves of an interval, shrunk and shifted to every scale and position (~engineeringkit.signal_processing.haar_transform). It was the first wavelet, though the word came 70 years later. Each Haar function lives on a short interval, so a jump in a signal touches only a few coefficients at each scale. A sine, by contrast, extends over all time and smears a jump over every coefficient. The transform keeps the signal&#x27;s energy and is inverted exactly (~engineeringkit.signal_processing.inverse_haar_transform).">

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  .. image:: /api/gallery/signal_processing/wavelets/images/thumb/sphx_glr_plot_01_haar_wavelet_thumb.png
    :alt:

  :doc:`/api/gallery/signal_processing/wavelets/plot_01_haar_wavelet`

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      <div class="sphx-glr-thumbnail-title">Haar's wavelet (1910)</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/signal_processing/wavelets/plot_01_haar_wavelet