Eckard,
"truly elementary insight based on common sense" That is exactly what the early FM radio engineers had, that physicists, enamored with Fourier analysis and orthogonal functions, have missed.
It is as simple as this:
(1) if a frequency-modulated signal is sent through a filter (like a resonator) with a sloping (non-flat) amplitude-vs-frequency response curve, then any change in frequency will be TRANSDUCED into a change in amplitude.
(2) This makes it possible to DETECT small frequency changes, without ever actually measuring either frequency or phase. Only simple-to-make amplitude measurements are necessary. But the output is ambiguous; a changing input amplitude, and not just a change in frequency, will also produce an change in the output amplitude.
(3) A simple procedure to eliminate this ambiguity, is to employ a pair of filters, with opposite slopes; taking the ratio of their output amplitudes will cancel out the effect of changes in the input amplitude, leaving a frequency-change as the only cause for a detector-output-amplitude change.
(4) This is how two-cone cells in the retina can produce the sensation of color, that is highly correlated with input frequency, even though the cone-cells are only sensitive to slow amplitude changes.
(5) What type of resonator-like bandpass filter has the minimum-possible time-bandwidth product? A Gaussian filter.
(6) How accurately does a pair of Gaussian filters, employed as above, enable the estimation of an input frequency? Exactly, unlike most other filter-types, that only yield an approximate estimate.
(7) This is all related to the Heisenberg uncertainty principle and Shannon's Capacity theorem, both of which are concerned with minimal time-bandwidth processes.
Rob McEachern