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

.. only:: html

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

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

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

.. _sphx_glr_generated_gallery_general_plot_SOI_filtering.py:


Applying a Filter to a Time-Series
==================================

This example demonstrates low pass filtering a time-series by applying a
weighted running mean over the time dimension.

The time-series used is the Darwin-only Southern Oscillation index (SOI),
which is filtered using two different Lanczos filters, one to filter out
time-scales of less than two years and one to filter out time-scales of
less than 7 years.

References
----------
    Duchon C. E. (1979) Lanczos Filtering in One and Two Dimensions.
    Journal of Applied Meteorology, Vol 18, pp 1016-1022.

    Trenberth K. E. (1984) Signal Versus Noise in the Southern Oscillation.
    Monthly Weather Review, Vol 112, pp 326-332

.. GENERATED FROM PYTHON SOURCE LINES 22-109



.. image-sg:: /generated/gallery/general/images/sphx_glr_plot_SOI_filtering_001.png
   :alt: Southern Oscillation Index (Darwin Only)
   :srcset: /generated/gallery/general/images/sphx_glr_plot_SOI_filtering_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    import iris
    import iris.plot as iplt


    def low_pass_weights(window, cutoff):
        """Calculate weights for a low pass Lanczos filter.

        Parameters
        ----------
        window : int
            The length of the filter window.
        cutoff : float
            The cutoff frequency in inverse time steps.

        """
        order = ((window - 1) // 2) + 1
        nwts = 2 * order + 1
        w = np.zeros([nwts])
        n = nwts // 2
        w[n] = 2 * cutoff
        k = np.arange(1.0, n)
        sigma = np.sin(np.pi * k / n) * n / (np.pi * k)
        firstfactor = np.sin(2.0 * np.pi * cutoff * k) / (np.pi * k)
        w[n - 1 : 0 : -1] = firstfactor * sigma
        w[n + 1 : -1] = firstfactor * sigma
        return w[1:-1]


    def main():
        # Load the monthly-valued Southern Oscillation Index (SOI) time-series.
        fname = iris.sample_data_path("SOI_Darwin.nc")
        soi = iris.load_cube(fname)

        # Window length for filters.
        window = 121

        # Construct 2-year (24-month) and 7-year (84-month) low pass filters
        # for the SOI data which is monthly.
        wgts24 = low_pass_weights(window, 1.0 / 24.0)
        wgts84 = low_pass_weights(window, 1.0 / 84.0)

        # Apply each filter using the rolling_window method used with the weights
        # keyword argument. A weighted sum is required because the magnitude of
        # the weights are just as important as their relative sizes.
        soi24 = soi.rolling_window("time", iris.analysis.SUM, len(wgts24), weights=wgts24)
        soi84 = soi.rolling_window("time", iris.analysis.SUM, len(wgts84), weights=wgts84)

        # Plot the SOI time series and both filtered versions.
        plt.figure(figsize=(9, 4))
        iplt.plot(
            soi,
            color="0.7",
            linewidth=1.0,
            linestyle="-",
            alpha=1.0,
            label="no filter",
        )
        iplt.plot(
            soi24,
            color="b",
            linewidth=2.0,
            linestyle="-",
            alpha=0.7,
            label="2-year filter",
        )
        iplt.plot(
            soi84,
            color="r",
            linewidth=2.0,
            linestyle="-",
            alpha=0.7,
            label="7-year filter",
        )
        plt.ylim([-4, 4])
        plt.title("Southern Oscillation Index (Darwin Only)")
        plt.xlabel("Time")
        plt.ylabel("SOI")
        plt.legend(fontsize=10)
        iplt.show()


    if __name__ == "__main__":
        main()


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

   **Total running time of the script:** (0 minutes 0.915 seconds)


.. _sphx_glr_download_generated_gallery_general_plot_SOI_filtering.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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