# [Eeglablist] Power Spectrum vs. Power Spectral Density

Ole Traupe ole.traupe at tu-berlin.de
Tue Jun 10 00:28:19 PDT 2014

```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>
An: 	Ole Traupe <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

Malvern, PA 19355

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

Malvern, PA 19355

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

Malvern, PA 19355

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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