Aliasing occurs when shifted versions of the spectrum of a sampled signal overlap, preventing perfect reconstruction.

Aliasing occurs when shifted versions of the spectrum of a sampled signal overlap, preventing perfect reconstruction.

• A. They never overlap.
• B. They overlap only if the sampling frequency is below twice the highest frequency.
• C. They overlap and prevent perfect reconstruction.
• D. They overlap only if the signal is not periodic.

Answer: (C)

Aliasing comes from the fact that when you sample a continuous signal, its spectrum copies appear at multiples of the sampling rate. If the signal’s bandwidth is too large relative to the sampling rate, these replicated spectra overlap. That overlap means different frequency components get folded into the same frequency range after sampling, so you can’t distinguish them from the samples alone. In short, the overlap is what causes aliasing, and when that happens you cannot perfectly reconstruct the original signal from the samples.

The condition for overlap is that the sampling rate is less than twice the signal’s maximum frequency. If you sample fast enough (fs ≥ 2Fmax), the copies don’t overlap and perfect reconstruction is possible with the right reconstruction filter. If the sampling rate is too low, overlap occurs and reconstruction is distorted.

The other options miss the essential link between overlap and reconstructability, or rely on incorrect ideas about when overlap occurs (such as connecting it to periodicity).