[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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>>
>>
>>
>> --
>> 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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