# In Fourier transforms, can momentum space be analogized to frequency, and position space be analogized to wavelength?

We know that in quantum mechanics, momentum space is the fourier transform of position space (and vice versa)

And also, in time-series analysis, that frequency (of cycles) is the fourier transform of the distribution of all cycle lengths.

What about electromagnetic radiation? Is the distribution of frequencies the Fourier transform of the distribution of wavelengths?

Is it physically feasible to think of a distribution of positions (each position value with a certain count), and then to take a fourier transform of that, and end up with a distribution of momentum values? Even in JPG compression, you have frequency and position (each position value has a certain count that corresponds to the color value on a scale of $0$ to $255$)

• Your question is not clear. The Fourier transform is a very well defined mathematical operation that decomposes a function into sines and cosines. It is up to you (or the field of science) to assign meaningful names/interpretations to the original domain and the transformed domain. So you end up with time/frequency or spacing/wavenumber, etc. If I have misunderstood your question, please clarify. Commented Sep 7, 2011 at 5:04
• Ah yes - it is up to the field of science to assign meaningful names/interpretations to the original domain and the transformed domain. What I was trying to ask was this: are there common features within the original domain, as compared to within the transformed domain? Commented Sep 7, 2011 at 5:28
• In other words, is "momentum" a "frequency" of position? Commented Sep 7, 2011 at 5:29