I understand that it is the mathematical function needed to interpret the data, but this makes no sense to me mathematically.Why must an electric field (as a function of time) be Fourier transformed to offer meaningful spectroscopic information? In other words:Why doesn't a computer simply interpret the raw data, how does the Fourier transformation mathematically make the data easier to interpret?

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I understand that it is the mathematical function needed to interpret the data, but this makes no sense to me mathematically.Why must an electric field (as a function of time) be Fourier transformed to offer meaningful spectroscopic information? In other words:Why doesn&#039;t a computer simply interpret the raw data, how does the Fourier transformation mathematically make the data easier to interpret?

yassou1v · Accepted Answer

Producing the frequency spectrum of a time series is nothing but doing a Fourier transform, that is obtaining the amplitudes (and phases) of sinusoidal waves which result in the time series when all summed together. Given a time series f(t) the Fourier amplitude in frequency space is  F  (  ω  )  =      ∫          −      ∞        ∞    d  t  f  (  t  )        e          −      i      ω      t        F  (  ω  ) is in general a complex function (containing not only the amplitude but also the relative phase shift of each wave component at frequency   ω). Its absolute value       |    F  (  ω  )      |   is the frequency spectrum and       |    F  (  ω  )            |        2   the power spectrum.In practice the time dependence is too complicated for a closed mathematical expression to exist for the Fourier transform, so it has to be calculated numerically. Many software packages for so called FFTs (Fast Fourier Transforms) exist. This is essentially what computers are doing when they obtain a spectrum from the raw data.

Why must an electric field be Fourier transformed to offer meaningful spectroscopic information?

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