Mathematically, you can do Fourier transform for all types of data.
What do you expect from Fourier transformation?
FT can give speed due to simultaneous signal processing. Additionally, improved accuracy, higher resolution, lower detection limit etc are desirable attributes of FT. But why then FT is not popular with other kinds of spectroscopies, whereas it is only done realised with IR.
Let me flip the question. Why is FT used with IR?
I know it is also used with periodic TEM images. That makes sense trying to determine the regular spacing (frequency).
In the 1980ies Fourier Analysis was investigates in the field of Auger electron spectroscopy. The idea was to separate contributions by their frequency:
- low frequency (drift in parameters, background),
- medium frequency (signal), and
- high frequency (noise)
It turned out that there are no well-defined frequencies for the different contribution and the spectra are not periodic (with energy), so you'll will not find Fourier transform there. The same holds for EDS, WDS.
In IR spectrometry often FTIR is used, where Fourier transform is part of the signal generation.
With FTIR there is no spectrum to look at before doing the Fourier transform, i.e. the Fourier transform is an integral part of the technology itself. Hence its name: Fourier Transform IR.
The other methods do not need any Fourier transforms, but one can of course use it if one wants to study the frequency contents and possibly filter away different types of noise (high and/or low frequencies).
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