.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/receiver/plot_01_pulse_shaping.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_receiver_plot_01_pulse_shaping.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_receiver_plot_01_pulse_shaping.py:


Nyquist pulse shaping and the eye diagram
=========================================

A root-raised-cosine (RRC) transmit filter followed by the same matched filter at
the receiver gives a raised-cosine overall response, whose zero crossings at every
other symbol instant cancel the intersymbol interference (Nyquist's criterion). The
roll-off :math:`\beta` trades bandwidth, :math:`(1 + \beta) R_s`, against the length
of the pulse tails and the sensitivity to timing errors — which the eye diagram shows.

.. GENERATED FROM PYTHON SOURCE LINES 11-33

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    import comnum
    from comnum.plot import BLUE

    SPS = 16
    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9.5, 3.8))
    for beta in [0.1, 0.35, 1.0]:
        h = comnum.pulse_shape("rc", SPS, n_taps=16 * SPS + 1, rolloff=beta)
        t = (np.arange(h.size) - h.size // 2) / SPS
        ax1.plot(t, h / h.max(), label=rf"$\beta$ = {beta}")
        H = np.abs(np.fft.fftshift(np.fft.fft(h, 4096)))
        f = np.fft.fftshift(np.fft.fftfreq(4096, 1 / SPS))
        ax2.plot(f, H / H.max(), label=rf"$\beta$ = {beta}")
    ax1.set(xlim=(-6, 6), xlabel="time (symbols)", title="raised-cosine pulse")
    ax1.set_xticks(range(-6, 7))
    ax2.set(xlim=(-1.2, 1.2), xlabel="frequency (symbol rate)", title="spectrum")
    ax2.legend()
    fig.tight_layout()




.. image-sg:: /auto_examples/receiver/images/sphx_glr_plot_01_pulse_shaping_001.png
   :alt: raised-cosine pulse, spectrum
   :srcset: /auto_examples/receiver/images/sphx_glr_plot_01_pulse_shaping_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 34-36

Eye diagrams of QPSK (in phase) after the RRC pair: wide open with a large roll-off,
narrower — and closing quickly with a timing error — with a small one.

.. GENERATED FROM PYTHON SOURCE LINES 36-50

.. code-block:: Python

    c = comnum.Constellation("qam", 4).normalized()
    _, x = comnum.symbols(c, 600, comnum.Rng(3))
    fig, axes = plt.subplots(1, 2, figsize=(9.5, 3.6), sharey=True)
    for ax, beta in zip(axes, [0.1, 0.5], strict=True):
        h = comnum.pulse_shape("rrc", SPS, n_taps=32 * SPS + 1, rolloff=beta)
        y = comnum.fir_filter(h, comnum.fir_filter(h, comnum.upsample(x, SPS)))
        y = y / np.sqrt(np.mean(np.abs(y[::SPS]) ** 2))
        # two-symbol windows centred on the sampling instants t = 0 and t = 1
        traces = y[40 * SPS - SPS // 2 : 560 * SPS - SPS // 2].real.reshape(-1, 2 * SPS)
        t = np.arange(2 * SPS) / SPS - 0.5
        ax.plot(t, traces.T, color=BLUE, linewidth=0.6, alpha=0.25)
        ax.set(title=rf"RRC pair, $\beta$ = {beta}", xlabel="time (symbols)", xlim=(-0.5, 1.5))
    axes[0].set_ylabel("in-phase amplitude")
    fig.tight_layout()



.. image-sg:: /auto_examples/receiver/images/sphx_glr_plot_01_pulse_shaping_002.png
   :alt: RRC pair, $\beta$ = 0.1, RRC pair, $\beta$ = 0.5
   :srcset: /auto_examples/receiver/images/sphx_glr_plot_01_pulse_shaping_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.274 seconds)


.. _sphx_glr_download_auto_examples_receiver_plot_01_pulse_shaping.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_pulse_shaping.ipynb <plot_01_pulse_shaping.ipynb>`

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

      :download:`Download Python source code: plot_01_pulse_shaping.py <plot_01_pulse_shaping.py>`

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

      :download:`Download zipped: plot_01_pulse_shaping.zip <plot_01_pulse_shaping.zip>`


.. only:: html

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

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