Discussion
A PM signal has index 1 and a \( 4 \ \mathrm{kHz} \) message. Its bandwidth is
Answer: D
Substituting into the rule:
\[ B = 2 \times 4(1+1) = 16 \ \mathrm{kHz} \]
so 16 kHz. 8 kHz is the narrowband limit, which an index of one is too large to justify. 12 kHz would follow from dropping a factor somewhere. And 4 kHz is the message frequency itself. An index of exactly one is a useful reference case, since the bandwidth is then precisely twice the narrowband figure and the arithmetic can be checked at a glance. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.
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