Discussion
A narrowband FM signal has \( \Delta f = 3 \ \mathrm{kHz} \) and \( f_m = 3 \ \mathrm{kHz} \). Carson's rule gives
Answer: D
Substituting equal values:
\[ B = 2(3+3) = 12 \ \mathrm{kHz} \]
so 12 kHz, and with an index of one this sits between the narrowband and wideband regimes. 6 kHz is twice the message frequency, the true narrowband limit which applies only when the index is much less than one. 3 kHz is the deviation. And 24 kHz doubles the correct answer. Recognising which regime a signal is in decides whether the simple limit or the full rule should be used.
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