What condition must the original signal satisfy to avoid aliasing when sampling at rate Fs?

What condition must the original signal satisfy to avoid aliasing when sampling at rate Fs?

• A. It must be zero for all frequencies.
• B. It must be strictly periodic.
• C. It must be bandlimited to less than Fs/2.
• D. It must be a power signal.

Answer: (C)

To avoid aliasing at the sampling rate Fs, the signal’s spectrum must fit entirely inside a band that does not cause overlapping of spectral copies created by sampling. That means the highest frequency present in the signal must be less than Fs/2. When you sample, the spectrum is replicated every Fs in the frequency domain; if any part of the original spectrum lies at or above Fs/2, these replicas overlap with the baseband, causing frequencies to masquerade as others—aliasing. Keeping the signal strictly bandlimited below Fs/2 prevents any overlap, so the original content can be reconstructed (assuming ideal filtering and no other distortions). The other options don’t address spectral content: having no frequencies at all is trivial and useless; being strictly periodic doesn’t guarantee no aliasing; and being a power signal has no bearing on the frequency content relevant to sampling.