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I have a time series (of 23 timestamps) of which I take the Fourier transform. Now the fourier transform has 23 imaginary values and each has an amplitude and a phase. When I get the phase angle, it given me arctan value of the angle. Now how can I determine if two fourier coefficients are in phase or out of phase.

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Depends on the phase reference point in time.

Depending on the reference point, every DFT basis sinusoid can be either in-phase or out-of-phase (by 180 degrees) with every other basis, thus the same with any coefficient weighting of these basis vectors.

If you reference phase to the center of a DFT (using an fftshift), then the angle will tell you whether a particular component has even or odd symmetry relative to the center.

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  • $\begingroup$ So in my case I get 23 complex values after fourier transform, I can check for each fourier coefficient that the phase would be arctan(imaginary_part/real_part). Now I have this value for all the coefficients. Can I compare these values to find if two coefficients are in phase or out of phase? $\endgroup$ – theharshest Apr 16 '14 at 5:08
  • $\begingroup$ Not without specifying a reference point. $\endgroup$ – hotpaw2 Apr 16 '14 at 5:59
  • $\begingroup$ can you please provide me a link where I can read more about finding the "reference point" or describe in brief here? $\endgroup$ – theharshest Apr 16 '14 at 7:09

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