Consider a mixture of different wavelengths being emitted from the same point (ex: a star). This light consists of a mixture of wavelengths and intensities at each wavelength. When measuring the combined signal as a time-series of amplitude values, we can then use something like Fourier Transform to get a frequency vs. power plot. Would this plot be a "physically" accurate description of what physical wavelengths are in the light, or is it somehow mathematically decomposed further.
I think... the same question - posed differently: Is it possible for the same combined waveform be generated by 2 distinct signals sources - with each source having its own set of emitted frequencies/intensities?
Suppose you have 1 star emitting at frequencies A, B, and C. Then another star emitting at frequencies J, K, and L. Is is somehow possible that the combined waveform (A+B+C) is the same as (J + K + L).