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I am trying to understand how Fourier transforms are used to make HNMR plots.

HNMR basically consists of hitting some molecules with some radiation and listening to the radio signal that results. This signal is then analyzed using the FFT and this results in a frequency versus intensity graph. Because the emitted radiation is sinusoidal the Fourier transformation gives you the frequency that the chemical shift of the molecules. (this is a very bad description of HNMR but it is a good enough description for my question).

I have exported the initial time signal data to Mathematica. I want to use the Fourier transform to recreate this frequency versus intensity plot from this time signal data. When I use the built in Mathematica DFT it gives me a set of real and complex values. Does anyone here know how I can turn that set of data into a spectrum? Does anyone know how those frequency plots take into account the complex part of the discrete Fourier transform?

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The complex values arise because you get phase information from the signal as well as frequency composition. If your interested in a power spectrum all you have to do is use the absolute value (some square it - depending on application) of the fourier transformed signal.

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  • $\begingroup$ Thank you. Searching around I found that the in HNMR spectra the absolute intensity at a given frequency is given by (RealPartofDFT^2+ComplexPartofDFT^2)^(1/2) $\endgroup$ May 2, 2015 at 2:34
  • $\begingroup$ that would be the absolute value of a complex number ;o) $\endgroup$
    – Martin
    May 2, 2015 at 20:12

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