Discussion
Why is the complex envelope the natural representation for a narrowband signal?
Answer: D
Because it splits the signal into the two parts that behave quite differently. The carrier is fast and carries no information; the envelope and phase vary slowly and carry all of it, so representing the signal as a slowly varying complex function times a known exponential is both compact and physically meaningful. Every simulation and every software radio works this way, sampling at a rate suited to the bandwidth rather than the carrier. It removes no noise, since noise within the band is carried through unchanged. It makes the representation complex rather than real. And frequency resolution depends on observation length, not on the representation chosen.
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