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)

Aliasing disappears when the spectrum of the original signal fits entirely inside the baseband that spans from -Fs/2 to Fs/2. This is the practical statement of the Nyquist–Shannon sampling theorem: to reconstruct the signal accurately from samples, the highest frequency present must be less than half the sampling rate. If any frequency components exceed Fs/2, those parts of the spectrum replicate around multiples of Fs and overlap with the baseband, causing high-frequency information to masquerade as lower frequencies. Making the signal strictly bandlimited to below Fs/2 guarantees the replicas do not overlap, so the original signal can be recovered without distortion. The other options don’t address spectral content and do not prevent overlap or relate to how sampling maps frequency components.