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 happens because sampling creates copies of the signal’s spectrum at multiples of the sampling frequency. When these shifted copies overlap in the frequency domain, different frequency components interfere with each other, so the original spectrum cannot be uniquely recovered from the samples. This overlap occurs when the sampling frequency is below twice the signal’s highest frequency, and in that case perfect reconstruction becomes impossible with standard reconstruction. Hence the statement that the shifted spectra overlap and prevent perfect reconstruction is the correct one. The other options misstate the overlap condition or the consequence: overlap does occur under certain sampling rates, it is not limited to nonperiodic signals, and simply saying overlap occurs without mentioning the reconstruction impact wouldn’t capture the full effect of aliasing.