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  <body bgcolor="#FFFFFF" text="#000000"><p><span style="padding: 3px 10px; border-radius: 5px; color: #ffffff; font-weight: bold; display: inline-block; background-color: #ff0000;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;External Email - Use Caution&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></p><p></p>
    <p>Yes, this is expected behavior -- downsampling is not decimating.</p>
    <p>When you discretely sample a continuous signal, you have your
      sample frequency sf (e.g. 1000 Hz) and your sample duration, which
      is basically assumed to be just 1/sf. There is no such thing as an
      instantaneous sample. So when you resample you try to approximate
      what would have happened had your original samples been
      bigger/slower. This is not the same as just dropping all the
      samples in the intervening intervening interval (which is also why
      resampling can take a little bit of time). <br>
    </p>
    <p>I think you've been assuming that you're resampling is like
      decimating. In decimating, you do just drop all the intervening
      data points. Many MNE objects support decimating. So if you want
      to go from an sf of 1000 Hz to 100Hz, then you decimate by a
      factor of 10, i.e. take only every tenth sample. Note that this
      generally a bad idea because it's very susceptible to aliasing and
      all sorts of other artefacts.</p>
    <p><a class="moz-txt-link-freetext" href="https://mne.tools/stable/overview/faq.html?highlight=faq#resampling-and-decimating-data">https://mne.tools/stable/overview/faq.html?highlight=faq#resampling-and-decimating-data</a><br>
    </p>
    <p>Best,</p>
    <p>Phillip<br>
    </p>
    <div class="moz-cite-prefix">On 23/08/2019 04:31, RODNEY PETRUS
      BALANDONG wrote:<br>
    </div>
    <blockquote type="cite"
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        <p class="MsoNormal"><span style="mso-fareast-language:EN-US">Dear
            Phillip,<o:p></o:p></span></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US">I
            resampled a signal that originally sampled at 1000Hz to a
            different frequency (i.e., 1000Hz, 800Hz, 100Hz). The three
            figures that attached with this email showed different
            sampling rate results in different magnitude for the signal
            at the same time.<o:p></o:p></span></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US">I
            understand from your explanation that this is expected where
            resampling will result in lose of temporal</span>
          resolution, so fast, high amplitude deviations are lost. But I
          notice from my experimentation; the amplitude deviation occurs
          throughout the resampled signal. Because of this, I am concern
          whether I performed the whole procedure properly or not. FYI,
          I would like to resample the signal into 100Hz.<o:p></o:p></p>
        <p class="MsoNormal"><o:p> </o:p></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US">The
            figure can be reproduced using the notebook that accessible
            from this
            <a
href="https://github.com/balandongiv/EyeCloseOpen/blob/master/HelpImportDownsample_EDF.ipynb"
              moz-do-not-send="true">
              link</a><o:p></o:p></span></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US">Dear
            Sebastion<o:p></o:p></span></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US">Thanks
            for the reply. Yes, it is about Nyquist Theorem. Thanks for
            the explanation, I really appreciate it.<o:p></o:p></span></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US">Regards<o:p></o:p></span></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US">Rodney<o:p></o:p></span></p>
        <p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
        <p class="MsoNormal"><b><span lang="EN-US">From:</span></b><span
            lang="EN-US"> Sebastián Castaño-Candamil
            <a class="moz-txt-link-rfc2396E" href="mailto:sebastian.castano@blbt.uni-freiburg.de">&lt;sebastian.castano@blbt.uni-freiburg.de&gt;</a>
            <br>
            <b>Sent:</b> Thursday, 22 August, 2019 5:13 PM<br>
            <b>To:</b> Discussion and support forum for the users of MNE
            Software <a class="moz-txt-link-rfc2396E" href="mailto:mne_analysis@nmr.mgh.harvard.edu">&lt;mne_analysis@nmr.mgh.harvard.edu&gt;</a>; RODNEY
            PETRUS BALANDONG <a class="moz-txt-link-rfc2396E" href="mailto:rodney.petrus_g03291@utp.edu.my">&lt;rodney.petrus_g03291@utp.edu.my&gt;</a><br>
            <b>Cc:</b> Phillip Alday <a class="moz-txt-link-rfc2396E" href="mailto:phillip.alday@mpi.nl">&lt;phillip.alday@mpi.nl&gt;</a>;
            <a class="moz-txt-link-abbreviated" href="mailto:mne_analysis@nmr.mgh.harvard.edu">mne_analysis@nmr.mgh.harvard.edu</a><br>
            <b>Subject:</b> Re: [Mne_analysis] Badly resample the signal<o:p></o:p></span></p>
        <p class="MsoNormal"><o:p> </o:p></p>
        <div>
          <p class="MsoNormal">Hi Rodney,<o:p></o:p></p>
        </div>
        <p class="MsoNormal"><o:p> </o:p></p>
        <div>
          <p class="MsoNormal">there isn't a way around that, i.e., it
            is a theoretical limitation, (I dont know exactly your
            background, and apologize in advance in case you already
            know this, but:) you cannot represent frequency components
            wit a frequency &gt; Fs/2, where Fs is your sampling
            frequency. In your case, you cannot analysis parts of the
            signal beyond 50Hz if you sample at 100<o:p></o:p></p>
        </div>
        <p class="MsoNormal"><o:p> </o:p></p>
        <div>
          <p class="MsoNormal">I do not know exactly what is the
            frequency of those fast variation, but I'd think that these
            are above 50ish Hz.<o:p></o:p></p>
        </div>
        <p class="MsoNormal"><o:p> </o:p></p>
        <div>
          <p class="MsoNormal">Hope that helps,<o:p></o:p></p>
        </div>
        <div>
          <p class="MsoNormal">Sebastián<o:p></o:p></p>
        </div>
        <p class="MsoNormal"><o:p> </o:p></p>
        <div>
          <table class="MsoNormalTable" cellspacing="0" cellpadding="0"
            border="0">
            <tbody>
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                <td style="padding:0cm 0cm 0cm 0cm">
                  <div>
                    <p class="MsoNormal"><strong><span
style="font-family:&quot;Calibri&quot;,sans-serif;mso-fareast-language:EN-US">Sebastian
                          Castaño-Candamil</span></strong><span
                        style="mso-fareast-language:EN-US"><o:p></o:p></span></p>
                  </div>
                  <div style="border:none;border-top:solid gray
                    1.5pt;padding:2.0pt 0cm 0cm 0cm;margin-top:2.25pt">
                    <p class="MsoNormal"><span
                        style="mso-fareast-language:EN-US">Doctorate
                        student<br>
                        Brain state decoding lab<br>
                        University of Freiburg<o:p></o:p></span></p>
                  </div>
                  <div style="margin-top:3.0pt;min-width:250px">
                    <div>
                      <div>
                        <p class="MsoNormal"><span
                            style="font-size:10.0pt;mso-fareast-language:EN-US">E
                            //
                          </span><span
                            style="mso-fareast-language:EN-US"><a
                              href="mailto:sebastian.castano@blbt.uni-freiburg.de"
                              moz-do-not-send="true"><span
                                style="font-size:10.0pt">sebastian.castano@blbt.uni-freiburg.de</span></a></span><span
style="font-size:10.0pt;mso-fareast-language:EN-US"><o:p></o:p></span></p>
                      </div>
                    </div>
                  </div>
                </td>
              </tr>
            </tbody>
          </table>
        </div>
        <div>
          <p class="MsoNormal">On Aug 22 2019, at 10:59 am, RODNEY
            PETRUS BALANDONG &lt;<a
              href="mailto:rodney.petrus_g03291@utp.edu.my"
              moz-do-not-send="true">rodney.petrus_g03291@utp.edu.my</a>&gt;
            wrote:<o:p></o:p></p>
        </div>
        <blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
          <div>
            <div>
              <p class="MsoNormal">  <o:p></o:p></p>
            </div>
            <div>
              <p class="MsoNormal"><span style="color:white">        External
                  Email - Use Caution        </span><o:p></o:p></p>
            </div>
            <p class="MsoNormal" style="margin-bottom:12.0pt"><o:p> </o:p></p>
            <div>
              <div>
                <p class="MsoNormal">I only interested with the signal
                  up to 100Hz, so it redundant and computationally
                  expensive to handle signal with 1000Hz.<o:p></o:p></p>
              </div>
              <p class="MsoNormal"><o:p> </o:p></p>
              <div>
                <p class="MsoNormal"> <o:p></o:p></p>
              </div>
              <p class="MsoNormal"><o:p> </o:p></p>
              <div>
                <p class="MsoNormal">I'm just curious whether ignoring
                  those brief high-frequency peaks will affect the
                  overall analysis later.  So, if  there is a way to
                  these brief high-frequency would be an advantage.<o:p></o:p></p>
              </div>
              <p class="MsoNormal"><o:p> </o:p></p>
              <div>
                <p class="MsoNormal"> <o:p></o:p></p>
              </div>
              <p class="MsoNormal"><o:p> </o:p></p>
              <div>
                <p class="MsoNormal">Anyhow, is it common practice to
                  neglect the brief high-frequency peaks?<o:p></o:p></p>
              </div>
              <p class="MsoNormal"><o:p> </o:p></p>
              <div>
                <p class="MsoNormal"> <o:p></o:p></p>
              </div>
              <p class="MsoNormal"><o:p> </o:p></p>
              <div>
                <div>
                  <div>
                    <div>
                      <p class="MsoNormal"><strong><span
                            style="font-family:&quot;Calibri&quot;,sans-serif">From:</span></strong>
                        Phillip Alday &lt;<a
                          href="mailto:phillip.alday@mpi.nl"
                          moz-do-not-send="true">phillip.alday@mpi.nl</a>&gt;<o:p></o:p></p>
                    </div>
                    <div>
                      <p class="MsoNormal"><strong><span
                            style="font-family:&quot;Calibri&quot;,sans-serif">Sent:</span></strong>
                        Thursday, 22 August, 2019 4:53 PM<o:p></o:p></p>
                    </div>
                    <div>
                      <p class="MsoNormal"><strong><span
                            style="font-family:&quot;Calibri&quot;,sans-serif">To:</span></strong>
                        RODNEY PETRUS BALANDONG &lt;<a
                          href="mailto:rodney.petrus_g03291@utp.edu.my"
                          moz-do-not-send="true">rodney.petrus_g03291@utp.edu.my</a>&gt;<o:p></o:p></p>
                    </div>
                    <div>
                      <p class="MsoNormal"><strong><span
                            style="font-family:&quot;Calibri&quot;,sans-serif">Cc:</span></strong>
                        <a
                          href="mailto:mne_analysis@nmr.mgh.harvard.edu"
                          moz-do-not-send="true">mne_analysis@nmr.mgh.harvard.edu</a><o:p></o:p></p>
                    </div>
                    <div>
                      <p class="MsoNormal"><strong><span
                            style="font-family:&quot;Calibri&quot;,sans-serif">Subject:</span></strong>
                        Re: [Mne_analysis] Badly resample signal<o:p></o:p></p>
                    </div>
                  </div>
                </div>
              </div>
              <div>
                <p class="MsoNormal"> <o:p></o:p></p>
              </div>
              <p class="MsoNormal"><o:p> </o:p></p>
              <div>
                <p class="MsoNormal">But why do you need to resample?
                  That's what I meant with an XY problem.<o:p></o:p></p>
              </div>
              <p class="MsoNormal"><o:p> </o:p></p>
              <div>
                <p class="MsoNormal">Why do you care about brief
                  high-frequency peaks?<o:p></o:p></p>
              </div>
              <p class="MsoNormal"><o:p> </o:p></p>
              <div>
                <p class="MsoNormal">Phillip<o:p></o:p></p>
              </div>
              <p class="MsoNormal"><o:p> </o:p></p>
              <div>
                <div>
                  <p class="MsoNormal">On 22/08/2019 11:46, RODNEY
                    PETRUS BALANDONG wrote:<o:p></o:p></p>
                </div>
              </div>
              <blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
                <div>
                  <p class="MsoNormal">I need to downsample an original
                    signal that sampled at 1000Hz to 100Hz.<o:p></o:p></p>
                </div>
                <p class="MsoNormal"><o:p> </o:p></p>
                <div>
                  <p class="MsoNormal"> <o:p></o:p></p>
                </div>
                <p class="MsoNormal"><o:p> </o:p></p>
                <div>
                  <div>
                    <div>
                      <div>
                        <p class="MsoNormal"><strong><span
                              style="font-family:&quot;Calibri&quot;,sans-serif">From:</span></strong>
                          Phillip Alday
                          <a href="mailto:phillip.alday@mpi.nl"
                            title="mailto:phillip.alday@mpi.nl"
                            moz-do-not-send="true">&lt;phillip.alday@mpi.nl&gt;</a><o:p></o:p></p>
                      </div>
                      <div>
                        <p class="MsoNormal"><strong><span
                              style="font-family:&quot;Calibri&quot;,sans-serif">Sent:</span></strong>
                          Thursday, 22 August, 2019 4:44 PM<o:p></o:p></p>
                      </div>
                      <div>
                        <p class="MsoNormal"><strong><span
                              style="font-family:&quot;Calibri&quot;,sans-serif">To:</span></strong>
                          RODNEY PETRUS BALANDONG
                          <a
                            href="mailto:rodney.petrus_g03291@utp.edu.my"
title="mailto:rodney.petrus_g03291@utp.edu.my" moz-do-not-send="true">
                            &lt;rodney.petrus_g03291@utp.edu.my&gt;</a><o:p></o:p></p>
                      </div>
                      <div>
                        <p class="MsoNormal"><strong><span
                              style="font-family:&quot;Calibri&quot;,sans-serif">Cc:</span></strong>
                          <a
                            href="mailto:mne_analysis@nmr.mgh.harvard.edu"
title="mailto:mne_analysis@nmr.mgh.harvard.edu" moz-do-not-send="true">
                            mne_analysis@nmr.mgh.harvard.edu</a><o:p></o:p></p>
                      </div>
                      <div>
                        <p class="MsoNormal"><strong><span
                              style="font-family:&quot;Calibri&quot;,sans-serif">Subject:</span></strong>
                          Re: [Mne_analysis] Badly resample signal<o:p></o:p></p>
                      </div>
                    </div>
                  </div>
                </div>
                <div>
                  <p class="MsoNormal"> <o:p></o:p></p>
                </div>
                <p class="MsoNormal"><o:p> </o:p></p>
                <div>
                  <p class="MsoNormal">Appropriate filtering may help
                    with some things, but .... I think we're heading
                    into XY question territory here (<a
                      href="http://xyproblem.info/"
                      title="http://xyproblem.info/"
                      moz-do-not-send="true">http://xyproblem.info/</a>).<o:p></o:p></p>
                </div>
                <p class="MsoNormal"><o:p> </o:p></p>
                <div>
                  <p class="MsoNormal">Why do you want to resample? What
                    are you trying to accomplish?<o:p></o:p></p>
                </div>
                <p class="MsoNormal"><o:p> </o:p></p>
                <div>
                  <p class="MsoNormal">Phillip<o:p></o:p></p>
                </div>
                <p class="MsoNormal"><o:p> </o:p></p>
                <div>
                  <div>
                    <p class="MsoNormal">On 22/08/2019 11:38, RODNEY
                      PETRUS BALANDONG wrote:<o:p></o:p></p>
                  </div>
                </div>
                <blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
                  <div>
                    <p class="MsoNormal">Dear Phillip,<o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <p class="MsoNormal"> <o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <p class="MsoNormal">Thanks for the response,<o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <p class="MsoNormal"> <o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <p class="MsoNormal">Just wonder whether there exist
                      different technique to address such an issue? For
                      example, rather than using the averaging approach<o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <p class="MsoNormal"> <o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <p class="MsoNormal">Regards<o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <p class="MsoNormal">Rodney<o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <p class="MsoNormal"> <o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <div>
                      <div>
                        <div>
                          <p class="MsoNormal"><strong><span
                                style="font-family:&quot;Calibri&quot;,sans-serif">From:</span></strong>
                            Phillip Alday
                            <a href="mailto:phillip.alday@mpi.nl"
                              title="mailto:phillip.alday@mpi.nl"
                              moz-do-not-send="true">&lt;phillip.alday@mpi.nl&gt;</a><o:p></o:p></p>
                        </div>
                        <div>
                          <p class="MsoNormal"><strong><span
                                style="font-family:&quot;Calibri&quot;,sans-serif">Sent:</span></strong>
                            Thursday, 22 August, 2019 4:33 PM<o:p></o:p></p>
                        </div>
                        <div>
                          <p class="MsoNormal"><strong><span
                                style="font-family:&quot;Calibri&quot;,sans-serif">To:</span></strong>
                            Discussion and support forum for the users
                            of MNE Software
                            <a
                              href="mailto:mne_analysis@nmr.mgh.harvard.edu"
title="mailto:mne_analysis@nmr.mgh.harvard.edu" moz-do-not-send="true">
                              &lt;mne_analysis@nmr.mgh.harvard.edu&gt;</a>;
                            RODNEY PETRUS BALANDONG <a
                              href="mailto:rodney.petrus_g03291@utp.edu.my"
title="mailto:rodney.petrus_g03291@utp.edu.my" moz-do-not-send="true">
                              &lt;rodney.petrus_g03291@utp.edu.my&gt;</a><o:p></o:p></p>
                        </div>
                        <div>
                          <p class="MsoNormal"><strong><span
                                style="font-family:&quot;Calibri&quot;,sans-serif">Subject:</span></strong>
                            Re: [Mne_analysis] Badly resample signal<o:p></o:p></p>
                        </div>
                      </div>
                    </div>
                  </div>
                  <div>
                    <p class="MsoNormal"> <o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <p class="MsoNormal">This is expected behavior for
                      resampling. With resampling, you lose temporal
                      resolution, so fast, high amplitude deviations are
                      lost.  This is what happens at the beginning of
                      your signal. Later in the signal you see that the
                      slower change in the mean of the signal is
                      preserved, but the bumps are list.<o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <p class="MsoNormal">Intuitively: you have fewer
                      samples, so you can't capture both the deviations
                      up and the deviations down, so they average out
                      and you get just the mean. So the big peak and big
                      trough early in your example just cancel out when
                      resampled.<o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <p class="MsoNormal">Phillip<o:p></o:p></p>
                  </div>
                  <p class="MsoNormal"><o:p> </o:p></p>
                  <div>
                    <div>
                      <p class="MsoNormal">On 22/08/2019 07:01, RODNEY
                        PETRUS BALANDONG wrote:<o:p></o:p></p>
                    </div>
                  </div>
                  <blockquote
                    style="margin-top:5.0pt;margin-bottom:5.0pt">
                    <div>
                      <p class="MsoNormal"><strong><span
                            style="font-family:&quot;Calibri&quot;,sans-serif;color:white">        External
                            Email - Use Caution        </span></strong><o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal">Dear All,<o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal"> <o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal">The issue is about sample
                        badly approximated<o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal"> <o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal">Given an original signal
                        sampled at 100Hz, the objective was to
                        downsampled it into 50 Hz<o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal">The downsampling process was
                        realised using the MNE resample.<o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal"> <o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal">However, as can be noticed
                        from the image below, the sample is badly
                        approximated. Instead of registering the
                        original signal magnitude, the function RESAMPLE
                        return an approximated signal magnitude.<o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal"> <o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal">This rise two question<o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <ol start="1" type="1">
                        <li class="MsoNormal"
                          style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l1
                          level1 lfo3">
                          Is it common for such badly resample to occur?<o:p></o:p></li>
                      </ol>
                    </div>
                    <div>
                      <ol start="2" type="1">
                        <li class="MsoNormal"
                          style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l1
                          level1 lfo3">
                          If yes, how to minimize this<o:p></o:p></li>
                      </ol>
                    </div>
                    <div>
                      <p class="MsoNormal"> <o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal">The problem can be reproduced
                        using the notebook which is accessible through
                        this
                        <a
href="https://github.com/balandongiv/EyeCloseOpen/blob/master/HelpImportDownsample_EDF.ipynb"
title="https://github.com/balandongiv/EyeCloseOpen/blob/master/HelpImportDownsample_EDF.ipynb"
                          moz-do-not-send="true">
                          link</a>.<o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal"> <o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal">Thanks in advance for
                        entertaining this request<o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal"> <o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal"> <o:p></o:p></p>
                    </div>
                    <p class="MsoNormal" style="margin-bottom:12.0pt"><br>
                      <br>
                      <o:p></o:p></p>
                    <div>
                      <p class="MsoNormal"> <o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal"> <o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal">Regards<o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <p class="MsoNormal">Rodney<o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><o:p> </o:p></p>
                    <div>
                      <div>
                        <p class="MsoNormal">DISCLAIMER : This e-mail
                          and any files transmitted with it ("Message")
                          is intended only for the use of the
                          recipient(s) named above and may contain
                          confidential information. You are hereby
                          notified that the taking of any action in
                          reliance upon, or any review, retransmission,
                          dissemination, distribution, printing or
                          copying of this Message or any part thereof by
                          anyone other than the intended recipient(s) is
                          strictly prohibited. If you have received this
                          Message in error, you should delete this
                          Message immediately and advise the sender by
                          return e-mail. Opinions, conclusions and other
                          information in this Message that do not relate
                          to the official business of Universiti
                          Teknologi PETRONAS (UTP) shall be understood
                          as neither given nor endorsed by Universiti
                          Teknologi PETRONAS (UTP).<o:p></o:p></p>
                      </div>
                      <p class="MsoNormal" style="margin-bottom:12.0pt"><br>
                        <br>
                        <o:p></o:p></p>
                    </div>
                    <p class="MsoNormal"><br>
                      <br>
                      <code><span style="font-size:10.0pt"><o:p></o:p></span></code></p>
                    <pre>_______________________________________________<o:p></o:p></pre>
                    <pre style="background-color:rgba(0,0,0,0.05)">Mne_analysis mailing list<o:p></o:p></pre>
                    <pre style="background-color:rgba(0,0,0,0.05)"><a href="mailto:Mne_analysis@nmr.mgh.harvard.edu" title="mailto:Mne_analysis@nmr.mgh.harvard.edu" moz-do-not-send="true">Mne_analysis@nmr.mgh.harvard.edu</a><o:p></o:p></pre>
                    <pre style="background-color:rgba(0,0,0,0.05)"><a href="https://mail.nmr.mgh.harvard.edu/mailman/listinfo/mne_analysis" title="https://mail.nmr.mgh.harvard.edu/mailman/listinfo/mne_analysis" moz-do-not-send="true">https://mail.nmr.mgh.harvard.edu/mailman/listinfo/mne_analysis</a><o:p></o:p></pre>
                  </blockquote>
                  <div>
                    <p class="MsoNormal">DISCLAIMER : This e-mail and
                      any files transmitted with it ("Message") is
                      intended only for the use of the recipient(s)
                      named above and may contain confidential
                      information. You are hereby notified that the
                      taking of any action in reliance upon, or any
                      review, retransmission, dissemination,
                      distribution, printing or copying of this Message
                      or any part thereof by anyone other than the
                      intended recipient(s) is strictly prohibited. If
                      you have received this Message in error, you
                      should delete this Message immediately and advise
                      the sender by return e-mail. Opinions, conclusions
                      and other information in this Message that do not
                      relate to the official business of Universiti
                      Teknologi PETRONAS (UTP) shall be understood as
                      neither given nor endorsed by Universiti Teknologi
                      PETRONAS (UTP).<o:p></o:p></p>
                  </div>
                </blockquote>
                <div>
                  <p class="MsoNormal">DISCLAIMER : This e-mail and any
                    files transmitted with it ("Message") is intended
                    only for the use of the recipient(s) named above and
                    may contain confidential information. You are hereby
                    notified that the taking of any action in reliance
                    upon, or any review, retransmission, dissemination,
                    distribution, printing or copying of this Message or
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                    received this Message in error, you should delete
                    this Message immediately and advise the sender by
                    return e-mail. Opinions, conclusions and other
                    information in this Message that do not relate to
                    the official business of Universiti Teknologi
                    PETRONAS (UTP) shall be understood as neither given
                    nor endorsed by Universiti Teknologi PETRONAS (UTP).<o:p></o:p></p>
                </div>
              </blockquote>
            </div>
            <div>
              <p class="MsoNormal">DISCLAIMER : This e-mail and any
                files transmitted with it ("Message") is intended only
                for the use of the recipient(s) named above and may
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                notified that the taking of any action in reliance upon,
                or any review, retransmission, dissemination,
                distribution, printing or copying of this Message or any
                part thereof by anyone other than the intended
                recipient(s) is strictly prohibited. If you have
                received this Message in error, you should delete this
                Message immediately and advise the sender by return
                e-mail. Opinions, conclusions and other information in
                this Message that do not relate to the official business
                of Universiti Teknologi PETRONAS (UTP) shall be
                understood as neither given nor endorsed by Universiti
                Teknologi PETRONAS (UTP).
                _______________________________________________<o:p></o:p></p>
            </div>
            <div>
              <p class="MsoNormal">Mne_analysis mailing list<o:p></o:p></p>
            </div>
            <div>
              <p class="MsoNormal"><a
                  href="mailto:Mne_analysis@nmr.mgh.harvard.edu"
                  moz-do-not-send="true">Mne_analysis@nmr.mgh.harvard.edu</a><o:p></o:p></p>
            </div>
            <div>
              <p class="MsoNormal"><a
                  href="https://mail.nmr.mgh.harvard.edu/mailman/listinfo/mne_analysis"
                  moz-do-not-send="true">https://mail.nmr.mgh.harvard.edu/mailman/listinfo/mne_analysis</a><o:p></o:p></p>
            </div>
          </div>
        </blockquote>
      </div>
      DISCLAIMER : This e-mail and any files transmitted with it
      ("Message") is intended only for the use of the recipient(s) named
      above and may contain confidential information. You are hereby
      notified that the taking of any action in reliance upon, or any
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