## Fourier Transform Power Spectrum

Input: sine wave at 10Hz, amplitude 1.

After the transform the plot has a spike at 10Hz with amplitude 0.5. If I vary the amplitude of the sine wave I get:

sine amp. - FT spike amp.
1 - 0.5
2 - 2
4 - 8

So it seems A' = A^2/2

Is this because power is proportional to A^2 and it is averaged over trough/crest so division by 2?
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 Are you adding real and imaginary parts? The power should be the same in both domains.
 Sorry I think I asked my question poorly. I'm doing this in a lab using LabVIEW and it's doing the FT. When I input a sine wave (vs time) with varied amplitude 'A', I get an output spike of amplitude (A^2)/2 centered at some fixed frequency. Is this because $P \propto A^2$? Is the half for 'average'? I'm just trying to make sense of what this VI is doing. All I know is "computes the averaged auto power spectrum of time signal". Does my data still make no sense? I'm not directly dealing with imaginary parts...

## Fourier Transform Power Spectrum

OK- you probably forgot to add the power in -ve and +ve frequencies.
 Take a look at http://en.wikipedia.org/wiki/Parseval%27s_theorem (applications)