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

.. only:: html

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

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

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

.. _sphx_glr_examples_raisedcosine.py:


===========================
Raised cosine filter design.
===========================

Design a raised cosine filter with a rolloff of 0.3.

.. GENERATED FROM PYTHON SOURCE LINES 8-26

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np
    from mplsignal import freqz_fir

    from fird.designer import FIRDesigner
    from fird.objective import RaisedCosineLinearObjective

    o = RaisedCosineLinearObjective(0.3)
    d = FIRDesigner(22, o)
    d.solve()
    h = d.get_impulse_response()
    fig, ax = plt.subplots()
    o.plot(ax, label="Desired")
    freqz_fir(h, ax=ax, magnitude_scale="linear", style="magnitude")
    ax.legend()
    fig.show()




.. image-sg:: /examples/images/sphx_glr_raisedcosine_001.png
   :alt: raisedcosine
   :srcset: /examples/images/sphx_glr_raisedcosine_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 27-28

Display the impulse response. As expected every other coefficient is close to zero and the middle coefficient is close to 0.5.

.. GENERATED FROM PYTHON SOURCE LINES 28-33

.. code-block:: Python

    print(h)
    fig, ax = plt.subplots()
    ax.stem(h)
    fig.show()




.. image-sg:: /examples/images/sphx_glr_raisedcosine_002.png
   :alt: raisedcosine
   :srcset: /examples/images/sphx_glr_raisedcosine_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    [-4.7770938e-08  1.1818022e-03  7.7605963e-09 -1.4592795e-02
      2.6864261e-08  3.6033765e-02 -3.1785043e-09 -8.7356219e-02
      2.4387249e-08  3.1164230e-01  4.9999998e-01  3.1164230e-01
      2.4387249e-08 -8.7356219e-02 -3.1785043e-09  3.6033765e-02
      2.6864261e-08 -1.4592795e-02  7.7605963e-09  1.1818022e-03
     -4.7770938e-08]




.. GENERATED FROM PYTHON SOURCE LINES 34-35

To make the coefficients exactly as expected, add a :class:`NyquistConstraint`

.. GENERATED FROM PYTHON SOURCE LINES 35-48

.. code-block:: Python


    from fird.constraint import NyquistConstraint  # noqa: E402

    c = NyquistConstraint(2)
    d = FIRDesigner(22, o, c)
    d.solve()
    h = d.get_impulse_response()
    fig, ax = plt.subplots()
    o.plot(ax, label="Desired")
    freqz_fir(h, ax=ax, magnitude_scale="linear", style="magnitude")
    ax.legend()
    fig.show()




.. image-sg:: /examples/images/sphx_glr_raisedcosine_003.png
   :alt: raisedcosine
   :srcset: /examples/images/sphx_glr_raisedcosine_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 49-50

Now, the every other coefficient is exactly zero.

.. GENERATED FROM PYTHON SOURCE LINES 50-55

.. code-block:: Python

    print(h)
    fig, ax = plt.subplots()
    ax.stem(h)
    fig.show()




.. image-sg:: /examples/images/sphx_glr_raisedcosine_004.png
   :alt: raisedcosine
   :srcset: /examples/images/sphx_glr_raisedcosine_004.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    [ 0.          0.0011818   0.         -0.01459281  0.          0.03603375
      0.         -0.08735623  0.          0.3116423   0.5         0.3116423
      0.         -0.08735623  0.          0.03603375  0.         -0.01459281
      0.          0.0011818   0.        ]




.. GENERATED FROM PYTHON SOURCE LINES 56-57

It is also possible to design root raised cosine filters

.. GENERATED FROM PYTHON SOURCE LINES 57-70

.. code-block:: Python


    from fird.objective import RootRaisedCosineLinearObjective  # noqa: E402

    o = RootRaisedCosineLinearObjective(0.3)
    d = FIRDesigner(12, o)
    d.solve()
    h = d.get_impulse_response()
    fig, ax = plt.subplots()
    o.plot(ax, label="Desired")
    freqz_fir(h, ax=ax, magnitude_scale="linear", style="magnitude")
    ax.legend()
    fig.show()




.. image-sg:: /examples/images/sphx_glr_raisedcosine_005.png
   :alt: raisedcosine
   :srcset: /examples/images/sphx_glr_raisedcosine_005.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 71-72

Here, the filter is not a Nyquist filter, but the convolution with itself should be.

.. GENERATED FROM PYTHON SOURCE LINES 72-79

.. code-block:: Python


    fig, ax = plt.subplots(2, 1)
    ax[0].stem(h, label="Root-raised cosine")
    ax[0].legend()
    ax[1].stem(np.convolve(h, h), label="Convolved with itself")
    ax[1].legend()
    fig.show()



.. image-sg:: /examples/images/sphx_glr_raisedcosine_006.png
   :alt: raisedcosine
   :srcset: /examples/images/sphx_glr_raisedcosine_006.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 1.663 seconds)


.. _sphx_glr_download_examples_raisedcosine.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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