[Eeglablist] Power Spectrum vs. Power Spectral Density

[Ole Traupe]

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

30 E. Swedesford Road

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

    30 E. Swedesford Road

    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

        30 E. Swedesford Road

        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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