Power Spectrum

[sanctus]

Does anyone have a good explanation or a good link to what the power spectrum is and how it is used and calculated?

[Erasmus00]

Does anyone have a good explanation or a good link to what the power spectrum is and how it is used and calculated?

 

Quite generally, a power spectrum is a signal's power plotted against pure sin wave frequencies. Usually you take a fourier transform of the signal to generate it. Without knowing more about the specific spectrum you are looking at, I can't answer more.

-Will

[Eclogite]

I'd like to state what Erasmus said, in a slightly different way, which may aid your understanding. (It will certainly aid mine.:evil: )

'Signals' (electromgnetic or sonic) are detected over a time interval. Signal strength will often be plotted against time. For many situations such a plot will appear complex, perhaps even chaotic, or random. Using Fourier Transforms the signal can be analysed and underlying (hidden) regular variations, sinusoidal in character, can be identified.

The power spectrum then shows the signal strength at each frequency. Thus the FT converts the data from a time domain to a frequency domain. This can be very useful for diagnostic purposes - for example, identifying the source of damaging vibrations in mechanical systems.

Hope that helps a little.

[Lithium]

The power spectrum is a fourier transform of the CMB in length scales as opposed to usual transforms in time. A common use for it is to create cosmological simulation boxes by applying some transformations, inverse transforming it and then applying a few more transformations. I know that was very descriptive so I will defer you to a paper (astro-ph/0503106) on this sort of thing.

You can calculate it using CMBFAST or you can observe it in the CMB.

[sanctus]

Erasmus, it is still general.

 

Eclogite and Erasmus you both speakd about singal strength and signal's power, how are these quantitities actually defined? The general definition I have applies for an arbitrary scalaer variable X in position space and goes like:

 

[math]\langle X(\bf{k},t_0)X*(\bf{k'},t_0)\rangle =(2\pi )^3 \delta (\bf{k}-\bf{k'})P_X (k)[/math]

 

Where the square brackets are the statistical average and the X(k,t0) are Fourier transforms in case of a flat universe...

 

Lithium I actually use CMBEASY but what is the use of calculating without grasping completely what you are calculating?

[Erasmus00]

Eclogite and Erasmus you both speakd about singal strength and signal's power, how are these quantitities actually defined?

 

To be fair, power is probably not quite the right word, usually you plot the intensity (power/area). The intensity of a given signal is proportional to its amplitude squared. The exact proportionality depends on the type of signal.

-Will