# Power at fundamental frequency

1. Jul 8, 2007

### maurom

Hi all,
reading an article I've encountered the concept of power at the fundamental frequency, google didn't help me. Could you please give to me any hint about this problem? It is at least one week I'm dealing to understand what the "fundamental power" is!!!
there is a kind of wave, express as:
Y(t)=a1*sin(omega*t)+b1*cos(omega*t)+a2*sin(2*omega*t)+b2*cos(2*omega*t)+a3*sin(3*omega*t)+b3*cos(3*omega*t)
they say that fundamental power is:
a1^2+b1^2
and the square error of the fundamental power is sqrt(2(SE(a1)^4 + SE(b1)^4))

to me it seems quite strange! The power of wave is the work/time, but I guess that the fundamental power it not related to the work/time meaning.
And anyway, how it can be approximated to the squared amplitudes???
also how the square error of fundamental power becomes the dirty thing I wrote above!!

thanks a lot,
Mauro

P.S the article is:
Methods for Diagnosis and Treatment. of Stimulus-Correlated Motion in Generic Brain Activation Studies Using fMRI.
www-bmu.psychiatry.cam.ac.uk/sitewide/publications/journal/bullmore99met.pdf
and the formula I'm talking about is at the beginning of page 42.

2. Jul 8, 2007

### mathman

It looks like the article is using a Fourier expansion of a signal with period omega. The first pair of terms is the fundamental, and the others are overtones (integer multiples of the fundamental).

3. Jul 8, 2007

### maurom

yes, it seems something derived from a fourier expansion, but actually the sum of sin and cos are there for other reasons. In fact, is to correct for interpolation errors aligning images: that comes from the work of Bullmore et al. cited just above the formula, and the frequency should be the frequency of the time series. By the way, this is not really important to answer my question, I guess!
I can not get the meaning of "power at a certain frequency", it doens't make any sense to me! Or at least, not in a physics way!!!!
I got a guessing answering to you.... maybe the power refers to the statistical power (http://en.wikipedia.org/wiki/Statistical_power) or the probability that a false positive doesn't occur!
may be....

4. Jul 8, 2007

### Claude Bile

Think of power at a certain frequency (or frequency interval) as the power you would get passing through a filter that only passes the frequency (or frequency interval) of interest.

Claude.