.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "signal_processor/plot_2_exponential.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_signal_processor_plot_2_exponential.py>`
        to download the full example code

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

.. _sphx_glr_signal_processor_plot_2_exponential.py:


Exponential Apodization
^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 7-22

In this example, we will use an exponential function to perform a Lorentzian
convolution to an example dataset. The exponential function
used for this apodization is defined as follows

.. math::

  f(x) = e^{-\sigma \pi |x|}

where :math:`\sigma` is parametrized by the the full width at half maximum as follows

.. math::

  \sigma = \frac{\text{FWHM}}{2 \sqrt{2 \ln{2}}}

Below we import the necessary modules

.. GENERATED FROM PYTHON SOURCE LINES 22-27

.. code-block:: default

    import csdmpy as cp
    import numpy as np
    from mrsimulator import signal_processor as sp









.. GENERATED FROM PYTHON SOURCE LINES 29-34

First we create ``processor``, an instance of the
:py:class:`~mrsimulator.signal_processor.SignalProcessor` class. The required
attribute of the SignalProcessor class, *operations*, is a list of operations to which
we add a :py:class:`~mrsimulator.signal_processor.apodization.Exponential` object
sandwiched between two Fourier transformations.

.. GENERATED FROM PYTHON SOURCE LINES 34-42

.. code-block:: default

    processor = sp.SignalProcessor(
        operations=[
            sp.IFFT(),
            sp.apodization.Exponential(FWHM="75 Hz"),
            sp.FFT(),
        ]
    )








.. GENERATED FROM PYTHON SOURCE LINES 43-46

Next we create a CSDM object with a test dataset which our signal processor will
operate on. Here, the dataset spans 500 Hz with a delta function centered at
0 Hz.

.. GENERATED FROM PYTHON SOURCE LINES 46-53

.. code-block:: default

    test_data = np.zeros(500)
    test_data[250] = 1
    csdm_object = cp.CSDM(
        dependent_variables=[cp.as_dependent_variable(test_data)],
        dimensions=[cp.LinearDimension(count=500, increment="1 Hz", complex_fft=True)],
    )








.. GENERATED FROM PYTHON SOURCE LINES 54-57

Now to apply the processor to the CSDM object, use the
:py:meth:`~mrsimulator.signal_processor.SignalProcessor.apply_operations` method as
follows

.. GENERATED FROM PYTHON SOURCE LINES 57-59

.. code-block:: default

    processed_dataset = processor.apply_operations(dataset=csdm_object).real








.. GENERATED FROM PYTHON SOURCE LINES 60-62

To see the results of the exponential apodization, we create a simple plot using the
``matplotlib`` library.

.. GENERATED FROM PYTHON SOURCE LINES 62-71

.. code-block:: default

    import matplotlib.pyplot as plt

    fig, ax = plt.subplots(1, 2, figsize=(8, 3.5), subplot_kw={"projection": "csdm"})
    ax[0].plot(csdm_object, color="black", linewidth=1)
    ax[0].set_title("Before")
    ax[1].plot(processed_dataset.real, color="black", linewidth=1)
    ax[1].set_title("After")
    plt.tight_layout()
    plt.show()



.. image-sg:: /signal_processor/images/sphx_glr_plot_2_exponential_001.png
   :alt: Before, After
   :srcset: /signal_processor/images/sphx_glr_plot_2_exponential_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.385 seconds)


.. _sphx_glr_download_signal_processor_plot_2_exponential.py:


.. only :: html

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



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

     :download:`Download Python source code: plot_2_exponential.py <plot_2_exponential.py>`



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

     :download:`Download Jupyter notebook: plot_2_exponential.ipynb <plot_2_exponential.ipynb>`


.. only:: html

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

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