[Eeglablist] Power Spectrum vs. Power Spectral Density

Ole Traupe ole.traupe at tu-berlin.de
Wed Jun 18 01:30:24 PDT 2014


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."

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?

Ole


Am 17.06.2014 17:37, schrieb Laszlo Balazs:
> Hi all,
> 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.
> Correct me if I am wrong.
> Best,
> Laszlo
>
> On 6/16/2014 9:53 PM, Makoto Miyakoshi wrote:
>> Thanks Ole. It was very informative for me!
>>
>> Makoto
>>
>>
>> On Tue, Jun 10, 2014 at 12:28 AM, Ole Traupe <ole.traupe at tu-berlin.de 
>> <mailto:ole.traupe at tu-berlin.de>> wrote:
>>
>>     HI all,
>>
>>     I forward a short discussion on this topic to the list showing
>>     that things always are more complicated.
>>
>>     Best,
>>     Ole
>>
>>
>>     -------- Original-Nachricht --------
>>     Betreff: 	RE: [Eeglablist] Power Spectrum vs. Power Spectral Density
>>     Datum: 	Thu, 5 Jun 2014 13:06:31 -0400 (EDT)
>>     Von: 	MICHAEL JOSEPH PIOVOSO <mjp5 at psu.edu> <mailto:mjp5 at psu.edu>
>>     An: 	Ole Traupe <ole.traupe at tu-berlin.de>
>>     <mailto:ole.traupe at tu-berlin.de>
>>
>>
>>
>>     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.
>>
>>     Michael J. Piovoso, Ph.D., P.E.
>>
>>     Professor of Electrical Engineering
>>
>>     Penn State University School of Graduate Professional Studies
>>
>>     30 E. Swedesford Road
>>
>>     Malvern, PA 19355
>>
>>     610-648-3356 <tel:610-648-3356>
>>
>>     *From:*Ole Traupe [mailto:ole.traupe at tu-berlin.de]
>>     *Sent:* Thursday, June 05, 2014 1:03 PM
>>     *To:* MICHAEL JOSEPH PIOVOSO
>>     *Subject:* Re: [Eeglablist] Power Spectrum vs. Power Spectral Density
>>
>>     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?
>>
>>     Ole
>>
>>     Am 05.06.2014 18:57, schrieb MICHAEL JOSEPH PIOVOSO:
>>
>>         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.
>>
>>         Michael J. Piovoso, Ph.D., P.E.
>>
>>         Professor of Electrical Engineering
>>
>>         Penn State University School of Graduate Professional Studies
>>
>>         30 E. Swedesford Road
>>
>>         Malvern, PA 19355
>>
>>         610-648-3356 <tel:610-648-3356>
>>
>>         *From:*Ole Traupe [mailto:ole.traupe at tu-berlin.de]
>>         *Sent:* Thursday, June 05, 2014 6:10 AM
>>         *To:* MICHAEL JOSEPH PIOVOSO
>>         *Subject:* Re: [Eeglablist] Power Spectrum vs. Power Spectral
>>         Density
>>
>>         Hi Micheal,
>>
>>         I think this is wrong. Anyhow, did you realize you replied
>>         only to me?
>>
>>         Ole
>>
>>
>>         Am 04.06.2014 21:10, schrieb MICHAEL JOSEPH PIOVOSO:
>>
>>             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.
>>
>>             Michael J. Piovoso, Ph.D., P.E.
>>
>>             Professor of Electrical Engineering
>>
>>             Penn State University School of Graduate Professional Studies
>>
>>             30 E. Swedesford Road
>>
>>             Malvern, PA 19355
>>
>>             610-648-3356 <tel:610-648-3356>
>>
>>             *From:*eeglablist-bounces at sccn.ucsd.edu
>>             <mailto:eeglablist-bounces at sccn.ucsd.edu>
>>             [mailto:eeglablist-bounces at sccn.ucsd.edu] *On Behalf Of
>>             *Ole Traupe
>>             *Sent:* Wednesday, June 04, 2014 5:34 AM
>>             *To:* eeglablist at sccn.ucsd.edu
>>             <mailto:eeglablist at sccn.ucsd.edu>
>>             *Subject:* Re: [Eeglablist] Power Spectrum vs. Power
>>             Spectral Density
>>
>>             Hi Brian, hi Makoto,
>>
>>             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).
>>
>>             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).
>>
>>             Ole
>>
>>
>>
>>             Am 03.06.2014 23:26, schrieb
>>             eeglablist-request at sccn.ucsd.edu
>>             <mailto:eeglablist-request at sccn.ucsd.edu>:
>>
>>                 Dear Brian,
>>
>>                 Actualy I did not know the difference. According to
>>                 wikipedia, spectral density is something like spectra
>>                 represented as cumulative distribution function.
>>
>>                 http://en.wikipedia.org/wiki/Spectral_density
>>
>>                 I don't know though when it is more appropriate to
>>                 use power spectra and spectral density... someone in
>>                 the list please help us.
>>
>>                 Makoto
>>
>>                 On Wed, May 28, 2014 at 8:50 AM, Erickson
>>                 <ericksonb.eng at gmail.com
>>                 <mailto:ericksonb.eng at gmail.com>> wrote:
>>
>>                 List,
>>
>>                 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,
>>
>>                 - Brian
>>
>>                 Applied Brain and Cognitive Sciences Program
>>
>>                 Drexel University
>>
>>
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>>
>>
>>
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>>
>>
>>
>> -- 
>> Makoto Miyakoshi
>> Swartz Center for Computational Neuroscience
>> Institute for Neural Computation, University of California San Diego
>
> -- 
>
> Laszlo Balazs, Ph.D.
> MTA Research Centre for Natural Sciences
> Institute of Cognitive Neuroscience and Psychology
>
> P O B 398, Budapest, Hungary, H-1394
> Tel:+36(1)382-6811
> http://www.cogpsyphy.hu/balazs

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