.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/signal_processing/plot_signal_processing_benchmark.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_api_gallery_signal_processing_plot_signal_processing_benchmark.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_signal_processing_plot_signal_processing_benchmark.py:


Aliasing before reconstruction
==============================

A 70 Hz cosine sampled at 100 Hz is indistinguishable from a 30 Hz cosine.
Checking the samples demonstrates why filtering after sampling cannot
recover the original frequency.

.. GENERATED FROM PYTHON SOURCE LINES 9-29



.. image-sg:: /api/gallery/signal_processing/images/sphx_glr_plot_signal_processing_benchmark_001.png
   :alt: plot signal processing benchmark
   :srcset: /api/gallery/signal_processing/images/sphx_glr_plot_signal_processing_benchmark_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.signal_processing import alias_frequency

    fs, frequency = 100, 70
    t = np.arange(20) / fs
    alias = alias_frequency(frequency, fs)
    assert np.isclose(alias, 30)
    np.testing.assert_allclose(np.cos(2 * np.pi * frequency * t), np.cos(2 * np.pi * alias * t), atol=1e-13)
    fine = np.linspace(0, t[-1], 2001)
    fig, ax = plt.subplots()
    ax.plot(fine, np.cos(2 * np.pi * frequency * fine), label="70 Hz")
    ax.plot(fine, np.cos(2 * np.pi * alias * fine), linestyle="--", label="30 Hz alias")
    ax.plot(t, np.cos(2 * np.pi * frequency * t), "ko", label="samples")
    ax.set(xlabel="time [s]", ylabel="amplitude")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.100 seconds)


.. _sphx_glr_download_api_gallery_signal_processing_plot_signal_processing_benchmark.py:

.. only:: html

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

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/signal_processing/plot_signal_processing_benchmark.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_signal_processing_benchmark.zip <plot_signal_processing_benchmark.zip>`


.. only:: html

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

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