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A signal band-limited to \( 4 \ \mathrm{kHz} \) must be sampled at no less than

  • A.2 kHz
  • B.16 kHz
  • C.8 kHz
  • D.4 kHz

Answer: C

The Nyquist rate is twice the highest frequency present:

\[ f_s \geq 2 \times 4 = 8 \ \mathrm{kHz} \]

so 8 kHz, and telephony indeed samples at 8 kHz for a 3.4 kHz channel with guard band. 4 kHz would alias the whole band. 2 kHz is worse still. 16 kHz is four times the highest frequency, which is perfectly usable and is oversampling by a factor of two, but it is not the minimum the question asks for.

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