The Gabor Limit states that it's impossible to simultaneously localize a signal in both frequency and time. FM communication modulates the instantaneous frequency of the carrier in step with changes in the signal. This suggests it's impossible to perfectly determine the instantaneous signal even in a theoretical channel with zero noise, or that one has to assume that the signal is changing slowly (band-limited). How is this overcome in practice? If demodulation requires the assumption of a band-limited signal, what is the maximum spectral efficiency of frequency modulation for a given input bandwidth?
EDIT: To clarify, this is a theoretical question. The Gabor Limit seems to imply that "instantaneous frequency" isn't well-defined if I understand it correctly. I'm not sure I do, though. The question boils down to:
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Do I understand the Gabor Limit correctly? Is "intantaneous frequency" an unmeasurable quantity?
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If I do understand the Gabor Limit correctly, how does FM modulation and demodulation work in spite of it? Is there a requirement that the demodulator assume that the signal being transmitted is band-limited even on a theoretical noise-free channel?
Best Answer
I'd turn this around and say it's impossible to instantaneously determine the signal.
In practice, our message signals are bandlimited, so this is not a difficulty. In fact, our message signals generally have much less bandwidth than the carrier.
To approach your theoretical question, is a band limit strictly required, Imagine trying to modulate a 1 Hz carrier with a 1 MHz signal --- the result would be unusable. So in fact there must be some kind of limit.