I collected spectrometric data which produced a graph with the intensity of each frequency of light.

  1. What more do I need to perform an inverse fourier transform of this data?

  2. Should I attempt an inverse discrete-fourier transform, or would it be easier to use a model so that I can do an inverse fast fourier transform for a composite function?

Note: I modelled the function using polynomials, a sigmoid function, a gaussian distribution, a sine wave, and a rational function

If anyone can assist I would be incredibly grateful Model: enter image description here

Discrete Data: enter image description here


What more do I need to perform an inverse Fourier transform of this data?

That really depends on WHY you want to do an inverse Fourier Transform. What do you expect the result to be and what do you use it for?

You certainly cannot get the actual time domain waveform of the light since you are missing phase and you are under-sampling by a factor of a billion or so.

Since what you have is essentially a power spectral density, you may get a estimate of the autocorrelation function. If you want to do this numerically you need

  1. Pick a sample rate
  2. Create an FFT grid
  3. Resample your existing frequency data so it fits on the grid
  4. Figure out what to do for the frequencies where you don't have information (extrapolate, roll off, zero out)
  5. Make it symmetric for negative frequencies
  6. Perform inverse FFT
  • $\begingroup$ Thank you so much! $\endgroup$ Jul 3 '21 at 8:27

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