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

.. only:: html

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

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

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

.. _sphx_glr_examples_finitewordlengthdesign.py:


=========================
Finite wordlength design.
=========================

It is almost always better to design filters taking the finite wordlength of the coefficients into account compared to rounding the coefficients after design.

.. GENERATED FROM PYTHON SOURCE LINES 8-16

.. 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 PiecewiseLinearObjective








.. GENERATED FROM PYTHON SOURCE LINES 17-18

First, design a filter minimizing the approximation error using a filter order of 31 and continuous coefficients as reference.

.. GENERATED FROM PYTHON SOURCE LINES 18-23

.. code-block:: Python

    o = PiecewiseLinearObjective([0, 0.3, 0.5, 1], [1, 1, 0, 0])
    d = FIRDesigner(31, o)
    d.solve()
    h31 = d.get_impulse_response()








.. GENERATED FROM PYTHON SOURCE LINES 24-25

Redesign the filter using ten fractional bits for the coefficients.

.. GENERATED FROM PYTHON SOURCE LINES 25-31

.. code-block:: Python


    fractional_bits = 10
    d = FIRDesigner(31, o, fractional_bits=fractional_bits)
    d.solve()
    h31_q = d.get_impulse_response()








.. GENERATED FROM PYTHON SOURCE LINES 32-35

Plot the resulting filters, including the rounded version of the continuous design.

As seen, the optimized finite wordlength design is better than the rounded continuous design.

.. GENERATED FROM PYTHON SOURCE LINES 35-55

.. code-block:: Python


    h31_rounded = np.round(h31 * 2**fractional_bits) / 2**fractional_bits

    fig, ax = plt.subplots()
    freqz_fir(h31_q, ax=ax, label="Optimized", style="magnitude")
    freqz_fir(h31_rounded, ax=ax, label="Rounded", style="magnitude")
    freqz_fir(h31, ax=ax, label="Continuous", style="magnitude")
    ax.set_ylim(-80, 5)
    ax.legend()
    axins = ax.inset_axes([0.1, 0.1, 0.3, 0.5])
    freqz_fir(h31_q, ax=axins, label="Optimized", style="magnitude")
    freqz_fir(h31_rounded, ax=axins, label="Rounded", style="magnitude")
    freqz_fir(h31, ax=axins, label="Continuous", style="magnitude")
    axins.set_xlim(0, 0.3 * np.pi)
    axins.set_ylim(-0.04, 0.04)
    axins.xaxis.label.set_visible(False)
    axins.yaxis.label.set_visible(False)
    ax.indicate_inset_zoom(axins, edgecolor="black")
    fig.show()




.. image-sg:: /examples/images/sphx_glr_finitewordlengthdesign_001.png
   :alt: finitewordlengthdesign
   :srcset: /examples/images/sphx_glr_finitewordlengthdesign_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 56-57

It is also possible to obtain the coefficients as an APyTypes fixed-point array.

.. GENERATED FROM PYTHON SOURCE LINES 57-59

.. code-block:: Python


    d.get_impulse_response(apytypes=True)




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

 .. code-block:: none


    APyFixedArray(
        [   1, 2047, 2045,    0,    7,    7, 2040, 2029, 2047,   32,   27, 2013, 1968, 2047,
          202,  383,  383,  202, 2047, 1968, 2013,   27,   32, 2047, 2029, 2040,    7,    7,
            0, 2045, 2047,    1],
        int_bits=1,
        frac_bits=10
    )




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

   **Total running time of the script:** (0 minutes 11.589 seconds)


.. _sphx_glr_download_examples_finitewordlengthdesign.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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