Discussion
A single tone 5 kHz message signal is sampled with 12 kHz, 8 kHz and 5 kHz. "Aliasing" effect will be observed in the reconstructed signal, when the 5 kHz signal is sampled with :
Answer: C
Aliasing occurs when the signal is sampled at both 8 kHz and 5 kHz.
The Nyquist criterion requires a sampling rate of at least twice the highest signal frequency:
\[ f_{s} \ge 2 f_{m} = 2 \times 5 = 10\ \text{kHz} \]
At 12 kHz the condition is met and the 5 kHz tone is recovered. At 8 kHz it appears as a false 3 kHz tone (8 - 5), and at 5 kHz it aliases to zero frequency, so both of these produce aliasing.
That rules out the options naming 12 kHz and the option saying aliasing never occurs.
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