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Is it possible to get relative phase information from Fourier analysis?

I am under the impression that * waves hands * Fourier analysis tells you the frequencies and amplitudes of the set of simple waveforms making up a more complex function.

This question came about by me looking at the Fourier toy. The circles at the bottom represent sinusoids of different frequencies. The radius represents the amplitude and the angle of the radius represents the phase shift of that sinusoid. Pretty cool.

So I use only two circles with an amplitude of 1, and by changing the phase of the first, I can get different resultant waveforms. That's really interesting to me.

I know that time shift of the overall function doesn't matter, since it's periodic, but there's gotta be a way to get the information out.

Please correct any incorrect notions I have. Thanks

user42630
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  • Some physical comments first: This strikes me as quite related to the phase problem which arises in x-ray diffraction measurements. (Which is, after all, basically an application of Fourier transform methods.) The challenge is that the usual measurements done there only give amplitudes, and one has to work hard to somehow obtain phases as well. – Semiclassical Aug 02 '14 at 16:15

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