<div dir="ltr">Thanks Ole. It was very informative for me!<div><br></div><div>Makoto</div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Tue, Jun 10, 2014 at 12:28 AM, Ole Traupe <span dir="ltr"><<a href="mailto:ole.traupe@tu-berlin.de" target="_blank">ole.traupe@tu-berlin.de</a>></span> wrote:<br>

<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
  

    
  
  <div text="#000000" bgcolor="#FFFFFF">
    HI all,<br>
    <br>
    I forward a short discussion on this topic to the list showing that
    things always are more complicated.<br>
    <br>
    Best,<br>
    Ole<br>
    <div><br>
      <br>
      -------- Original-Nachricht --------
      <table cellpadding="0" cellspacing="0" border="0">
        <tbody>
          <tr>
            <th valign="BASELINE" align="RIGHT" nowrap>Betreff:
            </th>
            <td>RE: [Eeglablist] Power Spectrum vs. Power Spectral
              Density</td>
          </tr>
          <tr>
            <th valign="BASELINE" align="RIGHT" nowrap>Datum: </th>
            <td>Thu, 5 Jun 2014 13:06:31 -0400 (EDT)</td>
          </tr>
          <tr>
            <th valign="BASELINE" align="RIGHT" nowrap>Von: </th>
            <td>MICHAEL JOSEPH PIOVOSO <a href="mailto:mjp5@psu.edu" target="_blank"><mjp5@psu.edu></a></td>
          </tr>
          <tr>
            <th valign="BASELINE" align="RIGHT" nowrap>An: </th>
            <td>Ole Traupe <a href="mailto:ole.traupe@tu-berlin.de" target="_blank"><ole.traupe@tu-berlin.de></a></td>
          </tr>
        </tbody>
      </table>
      <br>
      <br>
      
      
      
      <div>
        <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">What
            you say is correct.  The FFT gives what should be called the
            Energy Density (Not power density).   The units on the FFT
            are as you say for power density.   Common usage refers to
            it as a power density and also as a power spectral density. 
            But power spectral density is incorrect.  It is in fact an
            energy density not a power density.  The units are those of
            energy not power.<u></u><u></u></span></p>
        <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><u></u> <u></u></span></p>
        <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><u></u> <u></u></span></p>
        <div>
          <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Michael
              J. Piovoso, Ph.D., P.E.<u></u><u></u></span></p>
          <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Professor
              of Electrical Engineering<u></u><u></u></span></p>
          <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Penn
              State University School of Graduate Professional Studies<u></u><u></u></span></p>
          <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">30
              E. Swedesford Road<u></u><u></u></span></p>
          <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Malvern,
              PA 19355<u></u><u></u></span></p>
        </div>
        <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><a href="tel:610-648-3356" value="+16106483356" target="_blank">610-648-3356</a></span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><u></u><u></u></span></p>


        <div>
          <div style="border:none;border-top:solid #b5c4df 1.0pt;padding:3.0pt 0in 0in 0in">
            <p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext">
                Ole Traupe [<a href="mailto:ole.traupe@tu-berlin.de" target="_blank">mailto:ole.traupe@tu-berlin.de</a>] <br>
                <b>Sent:</b> Thursday, June 05, 2014 1:03 PM<br>
                <b>To:</b> MICHAEL JOSEPH PIOVOSO<br>
                <b>Subject:</b> Re: [Eeglablist] Power Spectrum vs.
                Power Spectral Density<u></u><u></u></span></p>
          </div>
        </div>
        <p class="MsoNormal"><u></u> <u></u></p>
        <p class="MsoNormal" style="margin-bottom:12.0pt">I am a
          psychologist and a programmer, and I clearly see your
          expertise here. I don't mean that there is a fundamental
          difference between the two. But there must be some kind of
          difference from my perspective, as the unit is different. No?
          In PS (unit^2), the values are power. In PSD (unit^2/Hz), the
          area under the curve is power. So you could probably say it's
          basically the same with PSD being somewhat transformed?<br>
          <br>
          Ole<br>
          <br>
          <u></u><u></u></p>
        <div>
          <p class="MsoNormal">Am 05.06.2014 18:57, schrieb MICHAEL
            JOSEPH PIOVOSO:<u></u><u></u></p>
        </div>
        <blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
          <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">If
              it is wrong, then  I have been teaching that for over 40
              years now and I need to understand the difference.  I
              check with other electrical engineers  and they agree with
              me.  I did not realize that it was sent to only you.  </span><u></u><u></u></p>
          <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"> </span><u></u><u></u></p>
          <div>
            <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Michael
                J. Piovoso, Ph.D., P.E.</span><u></u><u></u></p>
            <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Professor
                of Electrical Engineering</span><u></u><u></u></p>
            <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Penn
                State University School of Graduate Professional Studies</span><u></u><u></u></p>
            <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">30
                E. Swedesford Road</span><u></u><u></u></p>
            <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Malvern,
                PA 19355</span><u></u><u></u></p>
          </div>
          <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><a href="tel:610-648-3356" value="+16106483356" target="_blank">610-648-3356</a></span><u></u><u></u></p>


          <div>
            <div style="border:none;border-top:solid #b5c4df 1.0pt;padding:3.0pt 0in 0in 0in">
              <p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext">
                  Ole Traupe [<a href="mailto:ole.traupe@tu-berlin.de" target="_blank">mailto:ole.traupe@tu-berlin.de</a>]
                  <br>
                  <b>Sent:</b> Thursday, June 05, 2014 6:10 AM<br>
                  <b>To:</b> MICHAEL JOSEPH PIOVOSO<br>
                  <b>Subject:</b> Re: [Eeglablist] Power Spectrum vs.
                  Power Spectral Density</span><u></u><u></u></p>
            </div>
          </div>
          <p class="MsoNormal"> <u></u><u></u></p>
          <p class="MsoNormal" style="margin-bottom:12.0pt">Hi Micheal,<br>
            <br>
            I think this is wrong. Anyhow, did you realize you replied
            only to me?<br>
            <br>
            Ole<br>
            <br>
            <br>
            <u></u><u></u></p>
          <div>
            <p class="MsoNormal">Am 04.06.2014 21:10, schrieb MICHAEL
              JOSEPH PIOVOSO:<u></u><u></u></p>
          </div>
          <blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
            <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">There
                really is no difference between power spectral density
                and power spectrum.  Power spectral density is more
                correct but many use the term power spectrum for that as
                well.</span><u></u><u></u></p>
            <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"> </span><u></u><u></u></p>
            <div>
              <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Michael
                  J. Piovoso, Ph.D., P.E.</span><u></u><u></u></p>
              <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Professor
                  of Electrical Engineering</span><u></u><u></u></p>
              <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Penn
                  State University School of Graduate Professional
                  Studies</span><u></u><u></u></p>
              <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">30
                  E. Swedesford Road</span><u></u><u></u></p>
              <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Malvern,
                  PA 19355</span><u></u><u></u></p>
            </div>
            <p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><a href="tel:610-648-3356" value="+16106483356" target="_blank">610-648-3356</a></span><u></u><u></u></p>


            <div>
              <div style="border:none;border-top:solid #b5c4df 1.0pt;padding:3.0pt 0in 0in 0in">
                <p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext">
                    <a href="mailto:eeglablist-bounces@sccn.ucsd.edu" target="_blank">eeglablist-bounces@sccn.ucsd.edu</a>
                    [<a href="mailto:eeglablist-bounces@sccn.ucsd.edu" target="_blank">mailto:eeglablist-bounces@sccn.ucsd.edu</a>]
                    <b>On Behalf Of </b>Ole Traupe<br>
                    <b>Sent:</b> Wednesday, June 04, 2014 5:34 AM<br>
                    <b>To:</b> <a href="mailto:eeglablist@sccn.ucsd.edu" target="_blank">eeglablist@sccn.ucsd.edu</a><br>
                    <b>Subject:</b> Re: [Eeglablist] Power Spectrum vs.
                    Power Spectral Density</span><u></u><u></u></p>
              </div>
            </div><div class="">
            <p class="MsoNormal"> <u></u><u></u></p>
            <p class="MsoNormal" style="margin-bottom:12.0pt">Hi Brian,
              hi Makoto,<br>
              <br>
              as far as I know, and notwithstanding any considerations
              regarding a particular software implementation, the PS
              yields the power of a discrete, predefined set of
              frequencies interpretable as individual values. In
              contrast, similar to the probability density of the
              (standard) normal distribution, the PSD is a density
              function the (partial) area under which can be interpreted
              in terms of power. The transformation '10*log10' rescales
              to dB not affecting the units (i.e. unit^2 and unit^2/Hz,
              respectively).<br>
              <br>
              Therefore, the choice between PS and PSD depends on the
              question you want to answer. In EEG matters you are
              typically interested in the power of continuous frequency
              bands and therefore should consider the PSD (and determine
              the area within certain limits of interest).<br>
              <br>
              Ole<br>
              <br>
              <br>
              <br>
              <u></u><u></u></p>
            <div>
              <p class="MsoNormal">Am 03.06.2014 23:26, schrieb <a href="mailto:eeglablist-request@sccn.ucsd.edu" target="_blank">eeglablist-request@sccn.ucsd.edu</a>:<u></u><u></u></p>
            </div>
            </div><blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
              <div>
                <p class="MsoNormal">Dear Brian, <u></u><u></u></p><div class="">
                <div>
                  <p class="MsoNormal"> <u></u><u></u></p>
                </div>
                <div>
                  <p class="MsoNormal">Actualy I did not know the
                    difference. According to wikipedia, spectral density
                    is something like spectra represented as cumulative
                    distribution function.<u></u><u></u></p>
                </div>
                <div>
                  <p class="MsoNormal"> <u></u><u></u></p>
                </div>
                <div>
                  <p class="MsoNormal"><a href="http://en.wikipedia.org/wiki/Spectral_density" target="_blank">http://en.wikipedia.org/wiki/Spectral_density</a><u></u><u></u></p>
                </div>
                <div>
                  <p class="MsoNormal"> <u></u><u></u></p>
                </div>
                <div>
                  <p class="MsoNormal">I don't know though when it is
                    more appropriate to use power spectra and spectral
                    density... someone in the list please help us.<u></u><u></u></p>
                </div>
                <div>
                  <p class="MsoNormal"> <u></u><u></u></p>
                </div>
                <div>
                  <p class="MsoNormal">Makoto<u></u><u></u></p>
                </div>
              </div></div><div class="">
              <div>
                <p class="MsoNormal" style="margin-bottom:12.0pt"> <u></u><u></u></p>
                <div>
                  <p class="MsoNormal">On Wed, May 28, 2014 at 8:50 AM,
                    Erickson <<a href="mailto:ericksonb.eng@gmail.com" target="_blank">ericksonb.eng@gmail.com</a>>
                    wrote:<u></u><u></u></p>
                  <div>
                    <p class="MsoNormal">List, <u></u><u></u></p>
                    <div>
                      <p class="MsoNormal">The function "spectopo"
                        produces output in units of 10log_10 (uV^2/Hz).
                        This is power spectral density, as opposed to a
                        power spectrum. Could anyone comment on the
                        implications of interpreting, physiologically,
                        the PS vs. the PSD of a neural signal? Thank
                        you,<u></u><u></u></p>
                    </div>
                    <div>
                      <p class="MsoNormal"> <u></u><u></u></p>
                    </div>
                    <div>
                      <p class="MsoNormal">- Brian<u></u><u></u></p>
                    </div>
                    <div>
                      <p class="MsoNormal">Applied Brain and Cognitive
                        Sciences Program<u></u><u></u></p>
                    </div>
                    <div>
                      <p class="MsoNormal">Drexel University<u></u><u></u></p>
                    </div>
                  </div>
                  <p class="MsoNormal"><br>
                    _______________________________________________<br>
                    Eeglablist page: <a href="http://sccn.ucsd.edu/eeglab/eeglabmail.html" target="_blank">http://sccn.ucsd.edu/eeglab/eeglabmail.html</a><br>
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                    For digest mode, send an email with the subject "set
                    digest mime" to <a href="mailto:eeglablist-request@sccn.ucsd.edu" target="_blank">eeglablist-request@sccn.ucsd.edu</a><u></u><u></u></p>
                </div>
              </div>
            </div></blockquote>
            <p class="MsoNormal"> <u></u><u></u></p>
          </blockquote>
          <p class="MsoNormal"> <u></u><u></u></p>
        </blockquote>
        <p class="MsoNormal"><u></u> <u></u></p>
      </div>
      <br>
    </div>
    <br>
  </div>

<br>_______________________________________________<br>
Eeglablist page: <a href="http://sccn.ucsd.edu/eeglab/eeglabmail.html" target="_blank">http://sccn.ucsd.edu/eeglab/eeglabmail.html</a><br>
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-- <br><div dir="ltr">Makoto Miyakoshi<br>Swartz Center for Computational Neuroscience<br>Institute for Neural Computation, University of California San Diego<br></div>
</div>