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Michael, could you perhaps comment on that again? I am also a bit
confused. You stated below that "The units on the FFT are [...] for
power density.", but later you stated that "The units are those of
energy not power."<br>
<br>
So, does the FFT depend (in amplitude) on the length of a (uniform)
data vector and, thus, on the total energy of the data subject to
analysis?<br>
<br>
Ole<br>
<br>
<br>
<div class="moz-cite-prefix">Am 17.06.2014 17:37, schrieb Laszlo
Balazs:<br>
</div>
<blockquote cite="mid:53A060B4.7070809@ttk.mta.hu" type="cite">
<meta content="text/html; charset=ISO-8859-1"
http-equiv="Content-Type">
Hi all,<br>
Now I am getting confused. I believe that we are talking about
power (density) and not energy (density). PS is the squared
frequency spectrum (Fourier transform of the signal which has the
dimension of microvolts). The resulting dimension is uV^2
(microvolts squared) (or uV^2/Hz for density). Electrical power is
proportional with U^2 (P=U^2/R). Power is energy per unit of time,
or in other words, if it were energy than it were dependent of the
length of the period under question.<br>
Correct me if I am wrong.<br>
Best,<br>
Laszlo<br>
<br>
<div class="moz-cite-prefix">On 6/16/2014 9:53 PM, Makoto
Miyakoshi wrote:<br>
</div>
<blockquote
cite="mid:%3CCAEqC+SWbFemEsNvfY8z9_dDKzSzdV9GZ9TnhFGM7NuHqoikb9A@mail.gmail.com%3E"
type="cite">
<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 moz-do-not-send="true"
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="nowrap">Betreff: </th>
<td>RE: [Eeglablist] Power Spectrum vs. Power
Spectral Density</td>
</tr>
<tr>
<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
moz-do-not-send="true"
href="mailto:mjp5@psu.edu" target="_blank"><mjp5@psu.edu></a></td>
</tr>
<tr>
<th valign="BASELINE" align="RIGHT"
nowrap="nowrap">An: </th>
<td>Ole Traupe <a moz-do-not-send="true"
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.</span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"> </span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"> </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.</span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Professor
of Electrical Engineering</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</span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">30
E. Swedesford Road</span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Malvern,
PA 19355</span></p>
</div>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><a
moz-do-not-send="true" 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"></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 moz-do-not-send="true"
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</span></p>
</div>
</div>
<p class="MsoNormal"> </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>
</p>
<div>
<p class="MsoNormal">Am 05.06.2014 18:57, schrieb
MICHAEL JOSEPH PIOVOSO:</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></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"> </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.</span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Professor
of Electrical Engineering</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</span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">30
E. Swedesford Road</span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Malvern,
PA 19355</span></p>
</div>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><a
moz-do-not-send="true"
href="tel:610-648-3356" value="+16106483356"
target="_blank">610-648-3356</a></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 moz-do-not-send="true"
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></p>
</div>
</div>
<p class="MsoNormal"> </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>
</p>
<div>
<p class="MsoNormal">Am 04.06.2014 21:10,
schrieb MICHAEL JOSEPH PIOVOSO:</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></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"> </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.</span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Professor
of Electrical Engineering</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</span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">30
E. Swedesford Road</span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Malvern,
PA 19355</span></p>
</div>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><a
moz-do-not-send="true"
href="tel:610-648-3356"
value="+16106483356" target="_blank">610-648-3356</a></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">
<a moz-do-not-send="true"
href="mailto:eeglablist-bounces@sccn.ucsd.edu"
target="_blank">eeglablist-bounces@sccn.ucsd.edu</a>
[<a moz-do-not-send="true"
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 moz-do-not-send="true"
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></p>
</div>
</div>
<div class="">
<p class="MsoNormal"> </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>
</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"
target="_blank">eeglablist-request@sccn.ucsd.edu</a>:</p>
</div>
</div>
<blockquote
style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<p class="MsoNormal">Dear Brian, </p>
<div class="">
<div>
<p class="MsoNormal"> </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.</p>
</div>
<div>
<p class="MsoNormal"> </p>
</div>
<div>
<p class="MsoNormal"><a
moz-do-not-send="true"
href="http://en.wikipedia.org/wiki/Spectral_density"
target="_blank">http://en.wikipedia.org/wiki/Spectral_density</a></p>
</div>
<div>
<p class="MsoNormal"> </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.</p>
</div>
<div>
<p class="MsoNormal"> </p>
</div>
<div>
<p class="MsoNormal">Makoto</p>
</div>
</div>
</div>
<div class="">
<div>
<p class="MsoNormal"
style="margin-bottom:12.0pt"> </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:</p>
<div>
<p class="MsoNormal">List, </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,</p>
</div>
<div>
<p class="MsoNormal"> </p>
</div>
<div>
<p class="MsoNormal">- Brian</p>
</div>
<div>
<p class="MsoNormal">Applied Brain
and Cognitive Sciences Program</p>
</div>
<div>
<p class="MsoNormal">Drexel
University</p>
</div>
</div>
<p class="MsoNormal"><br>
_______________________________________________<br>
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</blockquote>
<p class="MsoNormal"> </p>
</blockquote>
<p class="MsoNormal"> </p>
</blockquote>
<p class="MsoNormal"> </p>
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</blockquote>
</div>
<br>
<br clear="all">
<div><br>
</div>
-- <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>
</blockquote>
<br>
<pre class="moz-signature" cols="72">--
Laszlo Balazs, Ph.D.
MTA Research Centre for Natural Sciences
Institute of Cognitive Neuroscience and Psychology
P O B 398, Budapest, Hungary, H-1394
<a moz-do-not-send="true" class="moz-txt-link-freetext" href="Tel:+36%281%29382-6811">Tel:+36(1)382-6811</a>
<a moz-do-not-send="true" class="moz-txt-link-freetext" href="http://www.cogpsyphy.hu/balazs">http://www.cogpsyphy.hu/balazs</a>
</pre>
</blockquote>
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