In a basic course of Electromagnetic Field, we arrived to introduce antennas. We studied the behaviour of the antenna by computing the electric field created when a sinusoidal input (the current flowing in a dipole) is applied to the dipole. I have a question: is this approach due to the fact that a generic signal (then, a generic current feeding the antenna) can be seen as a continuous sum of sinusoidal signals (Fourier Transform)? In this way, I should be able to apply superposition principle (at least in theory) for every sinusoidal component of the generic signal. And what about the electric field? I think it should be given (if my approach is correct) by the sum of an infinite number of plane waves, being each plane wave the effect of the corresponding sinusoidal component.
Can this principle (that is, to see a generic signal as the sum of sinusoidal signals, which should be always possible because phisical signals always have Fourier Transform) extended to other fields? For example, waveguides? As a consequence of my previous reasoning, when a video signal is applied to a coaxial cable, in the coaxial cable an infinite number of waves propagates: each wave should be the effect produced by a single sinusoidal component of the video signal.