Consider the following thought experiments:
Scenario 1:
A person standing far away shines 3 light beams at you, each beam having a narrow spectral distribution centered around different frequencies F1, F2, and F3. Where you stand, you have a sensor capable of perfectly sampling the combined (superimposed) waveform. If you do a Fourier Transform of the waveform picked up by the sensor, will you be able to recover the physical phenomena that contributed to the final waveform? In other words, would you be able to determine (1) There were exactly 3 light beams used and (2) The individual frequencies of each light beam were F1, F2, and F3. Or is it possible another combination of frequencies could produce the same waveform.
Scenario 2:
In this scenario, the person standing far away still shines 3 light beams, but there is no constraint that each one is emitting a single wavelength. For example, the first one might be a "yellow" beam emitting red and green frequencies. I am guessing in this scenario, we cannot possibly recover the actual physical phenomena; instead the observer would think the person far away has a separate red and green flashlight, as teh Fourier Analysis would decompose the wavelength into sinusoidal wavelengths.
Finally, is this ever an issue in real life? Can spectral measurements somehow mislead you as to the physical phenomena that is occuring?
Note: While I used visible light here as an example, I imagine this applies to any signal. As such, ignore any biological/subjective considerations concerning perception of color, etc.
