Background: I was taught that all electromagnetic radiation can be thought of as a sine wave, and that what we receive on a radio, for example, is actually the sum of sine waves over a range of frequencies. We can decompose a non-sinusoidal signal wave into its sine components and back via the Fourier transform.
I was also taught that all electromagnetic radiation can be quantized into photons with a particular frequency.
Question context: The first view of light as a continuous wave allows a continuity of the spectral decomposition. However the second view seems to indicate that this continuous spectrum must be discretized.
Question: How are the specific discretization of the power spectrum accomplished? If someone were broadcasting a signal with an infinite spectral decomposition (eg a square wave), would a receiver set up to detect individual photons detect photons of any frequency with a probability equal to the magnitude of the spectrum at that frequency?
Assuming that's the case, if we imagine individual photons being emitted from the transmitter, does each photon carry the probability of being detected over the full range of the signal, or does each photon have a very narrow range of uncertainty in its frequency? Does this narrowness depend on the rate at which photons are being emitted?