[Eeglablist] power spectrum versus power spectral density

Wed Jun 29 05:09:48 PDT 2016

Dear Kay,

thank you so much for your explanation! I am aware that - as you mentioned
- power and energy are very different concepts, energy being the capacity
to do work (calculated by integrating power over time), whereas power is
the rate, at which work is done or energy is transmitted.

   So, learning from you that PSD and power spectrum differ only in the
   normalization factor I still wonder:

   - what do we actually get out from averaging the power spectral density
   for a specific frequency range, coded as *mean(PSD(F>=fFreqency &
   F<=lastFreq))*; (e.g. fFreqency = 3.5 lastFrequency 7.5 for Theta)
      - would this be called "PSD for Theta?" Probably not? Is the direct
      output then microv^2/Hz?
      - papers reporting PSD instead of power spectrum plotted the complete
      power density without averaging the psd for a specific frequency range. I
      am though interested in the power of specific frequency band and
my initial
      preferation to use pwelch was its smoother power spectrum gain.

Agnieszka

2016-06-28 1:10 GMT+02:00 Kay Sung <ksung3 at jhmi.edu>:

> Hi,
>
>
>
> I had the same question about the power spectral density for myself and
> asked for some help in EEGlab list. Probably because of my lack of
> knowledge, I could not find very satisfactory explanation. But here is what
> I learned from various sources. (I’m not an electric engineer and may be
> wrong about many things.)
>
>
>
> The power spectral density is often expressed in watts/Hz and this unit in
> fact tells the amount of actual power of the signal. For now, forget about
> ‘/Hz’ term.
>
> Note that 1 watt is 1*V*I or 1*V^2/R.  Therefore, in electric engineering,
> to measure the power (watt), we need to know at least two of three terms
> (V, I, or R).  If we can somehow assume that R is constant, than V^2 is
> directly proportional to watt, the power. Note that power (e.g., watt) and
> energy (e.g., I, the electric current) are different things.
>
>
>
> The constant impedance may be true in electric hardware but not in human
> brain. In EEG setting, there is no way to know the exact amount of current
> (I) or impedance (R). The constant impedance is certainly not true. Given
> these situations in EEG, voltage is the only way to approximate the actual
> power (well, that’s the only thing we can measure) and the simplest measure
> of power is apparently V^2, which is known as absolute power. At this
> point, I do not know that we use V^2 as absolute power in EEG because we
> can assume R as relatively constant or simply because we don’t know R and
> decided to ignore it.  I know some people say as if the voltage is the
> measure of power but I think that is a mistake at least in EEG settings.
> The voltage is relatively defined by the amount of electric current (I) and
> impedance (i.e., V = IR) and watt is only available when we know at least
> two terms.
>
>
>
> Regarding the ‘/Hz’ term, we often use V^2/Hz as power measure (EEGlab
> calculates this when no baseline is subtracted for power calculation). As
> Dr. Horton explained before, the denominator (/Hz) is a normalization
> factor (the frequency bin size) and it is there so that the comparison of
> two different datasets is meaningful. This is because FFT may use different
> frequency bin size depending on the range of frequency in the data to be
> analyzed. The comparison of power based on FFT analysis will be meaningless
> if two datasets has different range of frequency.
>
>
>
> A side note. One of my questions I had before was whether we can express
> the spectral power (V^2/hz) as decibel. (at that time, I did not know the
> meaning of ‘/hz’.)  Makoto said we can, so it should be (J). It is
> basically the spectral power against a unit spectral power (V^2/Hz over 1
> V^2/Hz) and therefore we could say it is dB measure.
>
>
>
> Please correct any mistakes that I have in this posting. I’m still
> learning…
>
>
>
> K.
>
>
>
>
>
>
>
> *Kyongje (Kay) Sung, Ph.D*
>
> Research Associate
> *Johns Hopkins University School of Medicine*
> Cognitive Neurology & Neuropsychology – Department of Neurology
>
>
>
> 1629 Thames Street, Suite 350
>
> Baltimore, MD 21231
> P 443-287-8019 | F 410-955-0188
> ksung3 at jhmi.edu
> web.jhu.edu/cognitiveneurology/index.html
>
>
> _______________________________________________________________________________
>
> WARNING: This E-mail (including any attachments) is not secure.
> Information sent by e-mail may not remain
>
> confidential. This email may contain health care information. Permission
> to use or disclose this information has
>
> been granted either by law or the patient. Further use or disclosure
> without additional patient authorization or as
>
> otherwise permitted by law is prohibited.
>
> DISCLAIMER: This e-mail is intended only for the individual to whom it is
> addressed. It may be used only in
>
> accordance with applicable laws. If you received this e-mail by mistake,
> notify the sender and destroy the e-mail.
>
>
>
> Please consider the environment before printing this e-mail
>
>
> _______________________________________________________________________________
>
>
>
>
>
>
>
> *From:* eeglablist-bounces at sccn.ucsd.edu [mailto:
> eeglablist-bounces at sccn.ucsd.edu] *On Behalf Of *Agnieszka Zuberer
> *Sent:* Monday, June 27, 2016 9:40 AM
> *To:* EEGLAB List <eeglablist at sccn.ucsd.edu>
> *Subject:* [Eeglablist] power spectrum versus power spectral density
>
>
>
> Dear eeglab-community,
>
>
>
> for our resting baseline measurements we would like to compute the power
> for Theta, Alpha and Beta. In the eeglab-tutorial
> <http://ch.mathworks.com/help/signal/examples/practical-introduction-to-frequency-domain-analysis.html> we
> read that calculating the power spectral density with pwelch would yield
> a smoother power spectrum with power values closer to the expected values.
>
>
>
> Our questions are:
>
>    - What is the difference between power spectrum *(V^2/Hz)* and
>    power-spectral density *(**watts/Hz)* in lay terminology for a
>    non-electrophysiologist? Here we read tons of discussions on research gate
>    and other pages, but the difference was mainly defined in units instead of
>    really explaining the meaningful difference. Any literature on that would
>    be highly appreciated.
>    - what do we actually get out from averaging the power spectral
>    density for a specific frequency range, coded as *mean(PSD(F>=fFreqency
>    & F<=lastFreq))*; (e.g. fFreqency = 3.5 lastFrequency 7.5 for Theta)
>
>
>
> Thank you very much in advance.
>
> Agnieszka
>
>
>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://sccn.ucsd.edu/pipermail/eeglablist/attachments/20160629/07c6ae9f/attachment.html>