.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/convolution.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_convolution.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_convolution.py:

Simple Convolution Example
==========================
Since we use convolution a bit for signal analysis, test it here.

This also demonstrates the point that, when performing convolution, it's
important to distinguish between signals that are "causal" (like an FID --
consisting of real and imag that are Hermite transform pairs) vs. "non-causal"
(e.g. take the real part or the energy of a causal signal, or analyze a noise
PSD).
We show the time-domain signal by way of explanation as to how these are
treated differently.

.. GENERATED FROM PYTHON SOURCE LINES 13-39



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/images/sphx_glr_convolution_001.png
         :alt: Time domain
         :srcset: /auto_examples/images/sphx_glr_convolution_001.png, /auto_examples/images/sphx_glr_convolution_001_2_00x.png 2.00x
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_convolution_002.png
         :alt: Fourier transform
         :srcset: /auto_examples/images/sphx_glr_convolution_002.png, /auto_examples/images/sphx_glr_convolution_002_2_00x.png 2.00x
         :class: sphx-glr-multi-img


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

 .. code-block:: none

    1: Time domain |||s
    2: Fourier transform |||Hz







|

.. code-block:: Python

    from pylab import *
    from pyspecdata import *
    t = nddata(r_[0:4:1024j],'t').set_units('t','s')
    signal = exp(-1j*2*pi*100*t-20*t/pi)
    signal.add_noise(0.01)
    with figlist_var() as fl:
        fl.next('Time domain')
        fl.plot(signal, label='original')
        fl.next('Fourier transform', legend=True)
        signal.ft('t', shift=True)
        signal_real_copy = signal.real
        signal_real_copy_noncausal = signal.real
        fl.plot(signal, label='original')
        signal.convolve('t',5)
        signal_real_copy.convolve('t',5)
        signal_real_copy_noncausal.convolve('t',5, enforce_causality=False)
        fl.plot(signal, label='after convolve')
        fl.plot(signal_real_copy, label='real copy, after convolve')
        fl.plot(signal_real_copy_noncausal, ':', label='real copy, after convolve, treat as non-causal')
        fl.next('Time domain')
        signal.ift('t')
        signal_real_copy.ift('t')
        signal_real_copy_noncausal.ift('t')
        fl.plot(signal, label='after convolve')
        fl.plot(signal_real_copy, label='real copy, after convolve')
        fl.plot(signal_real_copy_noncausal, ':', label='real copy, after convolve, treat as non-causal')


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

   **Total running time of the script:** (0 minutes 1.006 seconds)


.. _sphx_glr_download_auto_examples_convolution.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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