Fourier Transform Spectroscopy - Converting Spectra From Time Domain To Frequency Domain

Converting Spectra From Time Domain To Frequency Domain

S(t) = \int_{-\infty}^\infty I(\nu) e^{- i\nu 2\pi t}\,d\nu

The sum is performed over all contributing frequencies to give a signal S(t) in the time domain.

I(\nu) = \int_{-\infty}^\infty S(t) e^{i\nu 2\pi t}dt

gives non-zero value when S(t) contains a component that matches the oscillating function.
Remember that

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