.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/signal_processing/spectral/plot_04_blackman_tukey_windows.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_spectral_plot_04_blackman_tukey_windows.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_spectral_plot_04_blackman_tukey_windows.py:


Blackman and Tukey's spectral windows (1958)
============================================

Ralph Blackman and John Tukey's *The Measurement of Power Spectra* (1958)
turned spectral estimation into an engineering procedure for the
telephone and seismic data of the Bell System. Cutting a finite record out
of a signal multiplies it by a rectangular window. In frequency, every
tone is then smeared by that window's transform, whose sidelobes fall
only slowly, so a strong tone can hide a weak one nearby. Their book named
the tapered windows of Julius von Hann and Richard Hamming that trade a
wider main lobe for far lower sidelobes
(:func:`~engineeringkit.signal_processing.windowed_spectrum`).

.. GENERATED FROM PYTHON SOURCE LINES 17-22

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.signal_processing import db20, windowed_spectrum








.. GENERATED FROM PYTHON SOURCE LINES 23-28

Each window's own spectrum
--------------------------

Zero-padding a constant record shows the window's transform. The highest
sidelobe sets how far below a strong tone a weak one can still be seen.

.. GENERATED FROM PYTHON SOURCE LINES 28-43

.. code-block:: Python


    fs, n = 1.0, 64
    expected = {"boxcar": -13.3, "hann": -31.5, "hamming": -42.7, "blackman": -58.1}
    fig, axes = plt.subplots(1, 2, figsize=(10, 3.8))
    for name, level in expected.items():
        f, magnitude = windowed_spectrum(np.ones(n), fs, window=name, n_fft=64 * n)
        response = db20(np.maximum(magnitude / magnitude[0], 1e-12))
        first_null = np.argmax(np.diff(response) > 0)  # end of the main lobe
        sidelobe = response[first_null:].max()
        print(f"{name:8s}: main lobe half-width {f[first_null] * n:.1f} bins, highest sidelobe {sidelobe:6.1f} dB")
        assert abs(sidelobe - level) < 0.5
        axes[0].plot(f * n, response, label=name)
    axes[0].set(xlabel="frequency [bins]", ylabel="gain [dB]", xlim=(0, 16), ylim=(-100, 5), title="Window transforms")
    axes[0].legend()




.. image-sg:: /api/gallery/signal_processing/spectral/images/sphx_glr_plot_04_blackman_tukey_windows_001.png
   :alt: Window transforms
   :srcset: /api/gallery/signal_processing/spectral/images/sphx_glr_plot_04_blackman_tukey_windows_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    boxcar  : main lobe half-width 1.0 bins, highest sidelobe  -13.3 dB
    hann    : main lobe half-width 2.0 bins, highest sidelobe  -31.5 dB
    hamming : main lobe half-width 2.0 bins, highest sidelobe  -42.4 dB
    blackman: main lobe half-width 3.0 bins, highest sidelobe  -58.1 dB

    <matplotlib.legend.Legend object at 0x1110474d0>



.. GENERATED FROM PYTHON SOURCE LINES 44-50

A weak tone near a strong one
-----------------------------

A tone 50 dB down sits six bins from a strong tone that falls between two
bins, the worst case for leakage. The rectangular window buries it; the
Blackman window reveals it.

.. GENERATED FROM PYTHON SOURCE LINES 50-69

.. code-block:: Python


    fs, n = 1024.0, 1024
    t = np.arange(n) / fs
    x = np.sin(2 * np.pi * 100.5 * t) + 10 ** (-50 / 20) * np.sin(2 * np.pi * 107 * t)
    visible = {}
    for name in ("boxcar", "blackman"):
        f, magnitude = windowed_spectrum(x, fs, window=name)
        level = db20(magnitude / magnitude.max())
        weak = level[np.argmin(abs(f - 107))]
        floor = np.max(level[(f > 104) & (f < 106)])
        visible[name] = weak > floor + 6
        print(f"{name:8s}: weak tone at {weak:6.1f} dB, leakage between the tones {floor:6.1f} dB")
        axes[1].plot(f, level, label=name)
    assert not visible["boxcar"] and visible["blackman"]
    axes[1].set(xlabel="frequency [Hz]", ylabel="level [dB]", xlim=(85, 125), ylim=(-120, 5), title="Strong tone at 100.5 Hz, weak at 107 Hz")
    axes[1].legend()
    fig.tight_layout()

    plt.show()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    boxcar  : weak tone at  -22.5 dB, leakage between the tones  -19.3 dB
    blackman: weak tone at  -48.8 dB, leakage between the tones  -58.1 dB





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

   **Total running time of the script:** (0 minutes 0.052 seconds)


.. _sphx_glr_download_api_gallery_signal_processing_spectral_plot_04_blackman_tukey_windows.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/spectral/plot_04_blackman_tukey_windows.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_04_blackman_tukey_windows.ipynb <plot_04_blackman_tukey_windows.ipynb>`

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

      :download:`Download Python source code: plot_04_blackman_tukey_windows.py <plot_04_blackman_tukey_windows.py>`

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

      :download:`Download zipped: plot_04_blackman_tukey_windows.zip <plot_04_blackman_tukey_windows.zip>`


.. only:: html

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

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