[Eeglablist] power spectrum versus power spectral density

[Makoto Miyakoshi]

Dear Agnieszka,

I'm not a signal processing engineer but let me share with you what I
learned from this mailing list (mostly from Andreas). Everyone, if I am
wrong please correct me.

Power spectral density (PSD): the longer the analysis window, the larger
the value because it's sum of the total signal length.

Power spectrum: PSD divided by signal length in second.

Thus, PSD of 1 second data == Power Spectrum.

> 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)

I believe using power spectrum makes sense almost all the time. Otherwise,
if subject A has twice longer recording time than subject B, the former
would show twice larger spectrum allover the broadband frequency, if my
understanding is correct.

Makoto



On Mon, Jun 27, 2016 at 6:40 AM, Agnieszka Zuberer <azuberer at googlemail.com>
wrote:

> 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
>
>
>
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-- 
Makoto Miyakoshi
Swartz Center for Computational Neuroscience
Institute for Neural Computation, University of California San Diego
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