Discussion
Coherent detection of DSB-SC requires a local carrier matched in
Answer: D
Both must match: a frequency error produces a beat and a phase error scales the output by its cosine, falling to zero when the reference is in quadrature with the signal. That quadrature null is the reason a phase-tracking loop is needed rather than a free-running oscillator. Amplitude of the reference affects only the output level. And no choice of intermediate frequency removes the need for a coherent reference. Keeping the carrier is a decision about the receiver, and keeping the second sideband a decision about the channel.
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