Fourier Transform Power Spectrum

[cscott]

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?

 

[christianjb]

Are you adding real and imaginary parts?

The power should be the same in both domains.

 

[cscott]

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...

 

[christianjb]

OK- you probably forgot to add the power in -ve and +ve frequencies.

 

[christianjb]

Take a look at http://en.wikipedia.org/wiki/Parseval's_theorem (applications)