[Eeglablist] Power Spectrum vs. Power Spectral Density

[Makoto Miyakoshi]

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>
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> <mjp5 at psu.edu>  An:
> Ole Traupe <ole.traupe at tu-berlin.de> <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
>
> *From:* Ole Traupe [mailto:ole.traupe at tu-berlin.de
> <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
>
> *From:* Ole Traupe [mailto:ole.traupe at tu-berlin.de
> <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
>
> *From:* eeglablist-bounces at sccn.ucsd.edu [
> mailto:eeglablist-bounces at sccn.ucsd.edu <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
> *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:
>
>  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> 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
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