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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>
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<th valign="BASELINE" align="RIGHT" nowrap="nowrap">Betreff:
</th>
<td>RE: [Eeglablist] Power Spectrum vs. Power Spectral
Density</td>
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<th valign="BASELINE" align="RIGHT" nowrap="nowrap">Datum: </th>
<td>Thu, 5 Jun 2014 13:06:31 -0400 (EDT)</td>
</tr>
<tr>
<th valign="BASELINE" align="RIGHT" nowrap="nowrap">Von: </th>
<td>MICHAEL JOSEPH PIOVOSO <a class="moz-txt-link-rfc2396E" href="mailto:mjp5@psu.edu"><mjp5@psu.edu></a></td>
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<tr>
<th valign="BASELINE" align="RIGHT" nowrap="nowrap">An: </th>
<td>Ole Traupe <a class="moz-txt-link-rfc2396E" href="mailto:ole.traupe@tu-berlin.de"><ole.traupe@tu-berlin.de></a></td>
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<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.<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></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.<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Professor
of Electrical Engineering<o:p></o:p></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<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">30
E. Swedesford Road<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Malvern,
PA 19355<o:p></o:p></span></p>
</div>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">610-648-3356</span><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p></o:p></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 class="moz-txt-link-freetext" href="mailto:ole.traupe@tu-berlin.de">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<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></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>
<o:p></o:p></p>
<div>
<p class="MsoNormal">Am 05.06.2014 18:57, schrieb MICHAEL
JOSEPH PIOVOSO:<o:p></o:p></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><o:p></o:p></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"> </span><o:p></o:p></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><o:p></o:p></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Professor
of Electrical Engineering</span><o:p></o:p></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><o:p></o:p></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">30
E. Swedesford Road</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Malvern,
PA 19355</span><o:p></o:p></p>
</div>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">610-648-3356</span><o:p></o:p></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 moz-do-not-send="true"
href="mailto:ole.traupe@tu-berlin.de">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><o:p></o:p></p>
</div>
</div>
<p class="MsoNormal"> <o:p></o:p></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>
<o:p></o:p></p>
<div>
<p class="MsoNormal">Am 04.06.2014 21:10, schrieb MICHAEL
JOSEPH PIOVOSO:<o:p></o:p></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><o:p></o:p></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"> </span><o:p></o:p></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><o:p></o:p></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Professor
of Electrical Engineering</span><o:p></o:p></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><o:p></o:p></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">30
E. Swedesford Road</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Malvern,
PA 19355</span><o:p></o:p></p>
</div>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">610-648-3356</span><o:p></o:p></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 moz-do-not-send="true"
href="mailto:eeglablist-bounces@sccn.ucsd.edu">eeglablist-bounces@sccn.ucsd.edu</a>
[<a moz-do-not-send="true"
href="mailto:eeglablist-bounces@sccn.ucsd.edu">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 moz-do-not-send="true"
href="mailto:eeglablist@sccn.ucsd.edu">eeglablist@sccn.ucsd.edu</a><br>
<b>Subject:</b> Re: [Eeglablist] Power Spectrum vs.
Power Spectral Density</span><o:p></o:p></p>
</div>
</div>
<p class="MsoNormal"> <o:p></o:p></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>
<o:p></o:p></p>
<div>
<p class="MsoNormal">Am 03.06.2014 23:26, schrieb <a
moz-do-not-send="true"
href="mailto:eeglablist-request@sccn.ucsd.edu">eeglablist-request@sccn.ucsd.edu</a>:<o:p></o:p></p>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<p class="MsoNormal">Dear Brian, <o:p></o:p></p>
<div>
<p class="MsoNormal"> <o:p></o:p></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.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><a moz-do-not-send="true"
href="http://en.wikipedia.org/wiki/Spectral_density">http://en.wikipedia.org/wiki/Spectral_density</a><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"> <o:p></o:p></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.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">Makoto<o:p></o:p></p>
</div>
</div>
<div>
<p class="MsoNormal" style="margin-bottom:12.0pt"> <o:p></o:p></p>
<div>
<p class="MsoNormal">On Wed, May 28, 2014 at 8:50 AM,
Erickson <<a moz-do-not-send="true"
href="mailto:ericksonb.eng@gmail.com"
target="_blank">ericksonb.eng@gmail.com</a>>
wrote:<o:p></o:p></p>
<div>
<p class="MsoNormal">List, <o:p></o:p></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,<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">- Brian<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">Applied Brain and Cognitive
Sciences Program<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">Drexel University<o:p></o:p></p>
</div>
</div>
<p class="MsoNormal"><br>
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<p class="MsoNormal"> <o:p></o:p></p>
</blockquote>
<p class="MsoNormal"> <o:p></o:p></p>
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