.. _sphx_glr_api_gallery_special_functions_z_transform:

Z-transform
-----------

Poles, zeros, stability, and inversion by partial fractions.


.. raw:: html

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


.. raw:: html

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

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Ragazzini and Zadeh&#x27;s 1952 Z-transform turns a difference equation into a rational function H(z). Each pole p contributes a mode p^n to the impulse response, so poles inside the unit circle decay and a pole outside grows without bound. Partial fractions invert H(z) term by term.">

.. only:: html

  .. image:: /api/gallery/special_functions/z_transform/images/thumb/sphx_glr_plot_01_poles_zeros_inverse_thumb.png
    :alt:

  :doc:`/api/gallery/special_functions/z_transform/plot_01_poles_zeros_inverse`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">The Z-transform: poles, stability, and partial fractions</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/special_functions/z_transform/plot_01_poles_zeros_inverse