[Eeglablist] power spectrum versus power spectral density

[Kay Sung]

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 (☺). 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<mailto:ksung3 at jhmi.edu>
web.jhu.edu/cognitiveneurology/index.html<http://web.jhu.edu/cognitiveneurology/index.html>
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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


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